Question

Is zeros of polynomial x square + PX + q all double in value to the the zeros of 2 x square - 5x -3 find the value of P and Q

Answer 1

Answer

The values of p and q are

$\boxed{\textbf{\large{p=-5}}}$

$\boxed{\textbf{\large{q=-6}}}$

Explanation

☑ let us consider the zeros of the polynomial [x^2+ px+q] are alpha and beta

☑ As we given, the zeros of the polynomial [x^2 + px + q ] are double in the value to the zeros of the polynomial [ 2x^2+5x-3]

☑ so consider the zeros of the polynomial [ 2x^2 +5x - 3] are

m and n

<> alpha = 2m ..........(1)

<> beta= 2n............(2)

so first, find the zeros of the polynomial 2x^2 - 5x - 3

2x^2 - 5x - 3

↪2x^2 -6x + 1x - 3

↪2x (x - 3 ) +1 ( x - 3 )

↪( 2x + 1 ) ( x - 3 )

x = -1/2 Or x = 3

zeroes are m = -1/2 and n = 3

so from (1) and (2) zeros of the polynomial x ^2 + px + q are

alpha= 2m = (-1/2)x 2 = -1

$\boxed{\textbf{\large{alpha=-1}}}$

beta = 2n = (3)x2 = 6

$\boxed{\textbf{\large{beta=6}}}$

we know ,

☑ if the roots of the equation are alpha and beta then the equation is x^2 -(alpha + beta) x +(alpha x beta)

we can write it as

x^2+(-(alpha + beta)x +(alpha x beta)

so compare the equation with

x^2 + px + q

p = -(alpha + beta)

q = (alpha x beta)

p=-(-1+6)=-5

q=(-1x 6) = -6

$\boxed{\textbf{\large{p=-5}}}$

$\boxed{\textbf{\large{q=-6}}}$

Answer 2

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Step-by-step explanation:

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