Question

If the zeros of the polynomial x2 + px + q are double in value to the zeros of 2x2 – 5x -3, find the values of p and q.

Answer 1

Answer

i hope its helpful for you

Step-by-step explanation:

Firstly we find the zeroes of p(x)= 2x² -5x -3 .

Zeroes are those values of x, for which polynomial p(x) = 0

So, 2x² - 5x -3 = 0

=> 2x² - 6x + x - 3 = 0

=> 2x(x-3) +1(x-3) = 0

=> ( x-3)(2x+1) = 0

=> x = 3 & -1/2

ie zeroes are 3 & -1/2 . . . . . . . . . . . . . . (1)

Now, zeroes £ & β, of S(x) = x² + px + q will be

3x2= 6

& (-1/2)x 2 = -1

ie, £ = 6 & β = -1

So, polynomial S(x) = (x- £)(x-β)

= (x- 6)(x+1)

= x² -6x+ x-6

= x² - 5x -6 = x² + px + q

By equating coefficients

P= -5 & q = -6