If -4 is a root of the equationx2 + px – 4 = 0 and if the equationx2

1.	If -4 is a root of the equationx2 + px – 4 = 0 and if the equationx2 + px + q = 0 has equal roots, find the values of p and q.
Answer» Let p(x) = x² + px – 4 – 4 is the root of the equation P(-4) = 0 16 – 4p – 4 = 0 -4p + 12 = 0 -4p = -12 p = 12/4 = 3 The equation x² + px + q = 0 has equal roots x² + 3 x + q = 0 Here a = 1, b = 3, c = q Since the roots are real and equal b² – 4 ac = 0 3² – 4(1)(q) = 0 9 – 4q = 0 9 = 4q q = 9/4 The value of p = 3 and q = 9/4

If -4 is a root of the equationx2 + px – 4 = 0 and if the equationx2 + px + q = 0 has equal roots, find the values of p and q.

Answer»

Let p(x) = x² + px – 4

– 4 is the root of the equation

P(-4) = 0

16 – 4p – 4 = 0

-4p + 12 = 0

-4p = -12

p = 12/4 = 3

The equation x² + px + q = 0 has equal roots

x² + 3 x + q = 0

Here a = 1, b = 3, c = q

Since the roots are real and equal

b² – 4 ac = 0

3² – 4(1)(q) = 0

9 – 4q = 0

9 = 4q

q = 9/4

The value of p = 3 and q = 9/4