Quadratic Equations

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

It is given that −3 is a root of 5 (x + k)² − 20 = 0, where k is a constant. Find the possible values of k.

• 1 or 5

• 1 or −7

• −1 or −5

• −1 or 7

Find the value of x in the figure.

• 2

• 3

• 4

• 5

Let x be the larger one of two consecutive odd numbers. If the sum of the squares of the two odd numbers is less than four times the product of the two odd numbers by 2, then

• x² + (x − 1)² = 4x (x − 1) + 2

• x² + (x − 1)² = 4x (x − 1) −2

• x² + (x − 2)² = 4x (x − 2) + 2

• x² + (x − 2)² = 4x (x − 2) −2

Which of the following equations have real roots?

I. 3x² − 7x + 5 = 0

II. 4x² + x = 3

III. x² + 12x = 2x − 25

• I and II only

• I and III only

• II and III only

• I, II and III

If the quadratic equation x² − 8x + p = 0 has no real roots, find the range of values of p.

• p < 12

• p > 12

• p < 16

• p > 16

If the quadratic equation x² + (8 − k)x + 9 = 0 has one double real root, then k =

• −2

• 2

• −2 or 14

• 2 or 14

If α and β are the roots of the quadratic equation x² − 6x + (k + 2) = 0 and 2/α + 2/β = 3/2, find the value of k.

• 1

• 2

• 4

• 6

Find the value of a² + b² from the above.

• −14

• −5

• 4

• 22