Maths4U Original · Short practice

Let \(P(x)=3 x^{2} + 11 x - 20\).

Find the positive solution of \(\displaystyle P(x)=0\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=4 x^{2} + 19 x - 30\).

Find the positive solution of \(\displaystyle P(x)=0\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=4 x^{2} + 19 x - 30\).

Find the negative solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=5 x^{2} + 4 x - 12\).

Find the negative solution.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=5 x^{2} + 4 x - 12\).

Find the constant term of P.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=2 x^{2} + 3 x - 9\).

Find the constant term of P.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=2 x^{2} + 3 x - 9\).

Find the sum of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(P(x)=3 x^{2} + 8 x - 16\).

Find the sum of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=3 x^{2} - 30 x + 79\).

Find the x-coordinate of the vertex.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=4 x^{2} - 48 x + 149\).

Find the x-coordinate of the vertex.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=4 x^{2} - 48 x + 149\).

Find the minimum value of f.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=x^{2} - 2 x + 7\).

Find the minimum value of f.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=x^{2} - 2 x + 7\).

Find f at one unit to the right of its vertex.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=2 x^{2} - 8 x + 15\).

Find f at one unit to the right of its vertex.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=2 x^{2} - 8 x + 15\).

Find the y-intercept of the graph.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

For real x, \(f(x)=3 x^{2} - 18 x + 35\).

Find the y-intercept of the graph.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 5 x - 7 = 0\). Decimal approximations are requested only where explicitly stated.

Find the discriminant.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 6 x - 8 = 0\). Decimal approximations are requested only where explicitly stated.

Find the discriminant.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 6 x - 8 = 0\). Decimal approximations are requested only where explicitly stated.

Find the sum of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 7 x - 9 = 0\). Decimal approximations are requested only where explicitly stated.

Find the sum of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 7 x - 9 = 0\). Decimal approximations are requested only where explicitly stated.

Find the product of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 8 x - 10 = 0\). Decimal approximations are requested only where explicitly stated.

Find the product of the two roots.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 8 x - 10 = 0\). Decimal approximations are requested only where explicitly stated.

Find the minimum value of the quadratic expression.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Solve \(x^{2} + 2 x - 2 = 0\). Decimal approximations are requested only where explicitly stated.

Find the minimum value of the quadratic expression.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.