Question

Find the value of p and q if the zeros of the polynomial x2 + px + q are twice the zeros of the polynomial 2x2-5x - 3.​

Answer 1

Answer:

p = -5, q = -6

Step-by-step explanation:

2x²-5x-3 = 2x²-6x+x-3

              = 2x(x-3)+1(x-3)

              = (x-3)(2x+1)

Hence, the zeros of 2x²-5x-3 are -1/2 and 3.

Zeros of the polynomial x²+px+q  are double in value to -1/2 and 3,

Thus zeros are -1 and 6.

Now, quadratic expression with zeros -1 and 6 is given by

(x + 1)(x-6) = x²-5x-6. By comparison, p = -5 and q = -6.

Answer 2

Answer:

Step-by-step explanation:

p = -5, q = -6

Step-by-step explanation:

2x²-5x-3 = 2x²-6x+x-3

             = 2x(x-3)+1(x-3)

             = (x-3)(2x+1)

Hence, the zeros of 2x²-5x-3 are -1/2 and 3.

Zeros of the polynomial x²+px+q  are double in value to -1/2 and 3,

Thus zeros are -1 and 6.

Now, quadratic expression with zeros -1 and 6 is given by

(x + 1)(x-6) = x²-5x-6. By comparison, p = -5 and q = -6.