Quadratic Equations

If α and β are the roots of the quadratic equation x² + 4x − 7 = 0, form a quadratic equation in x whose roots are α − 1 and β − 1.

• x² + 6x − 14 = 0

• x² + 6x − 2 = 0

• x² − 6x − 2 = 0

• x² − 6x − 14 = 0

In the figure, the curve y = x² + px + q cuts the x-axis at two points A(α, 0) and B(β, 0). M(−2, 0) is the mid-point of AB. (a) Express α + β in terms of p.

In the figure, the curve y = x² + px + q cuts the x-axis at two points A(α, 0) and B(β, 0). M(−2, 0) is the mid-point of AB.

(a) ii) Hence, find the value of p.

In the figure, the graph of y = x² + kx + 3 cuts the x-axis at two points A and B. If the distance between A and B is 2 units, find the value of k.

The roots of the equation 2x² − x − 6 = 0 are

• 3/2 , 5

• −2 , ½

• −3/2 , 2

• 3 , −3/2

Solve the equation (x − k)² - k² = 0

• k

• 2k

• 0 or 2k

• 0 or −2k

Which of the following equations have real roots?

• I and II only

• I and III only

• II and III only

• I, II and III

In the figure, the curve y = x² + px + q cuts the x-axis at two points A(α, 0) and B(β, 0). M(−2, 0) is the mid-point of AB. (b) If α² + β² = 26, find the value of q.

In the figure, the graph of y = x² + kx + 3 cuts the x-axis at two points A and B. If the distance between A and B is 2 units,(b) find the coordinates of the mid-point M of A and B.

What is the vertex of the graph shown above?

• (7,6)

• (-1,2)

• (2,-1)

• (5,0)