Question

If p(x) = 4 x^2 -3x x^3 +5 and q(x) = x^2 + 2 x +4 , then p(x) - q(x) is ..... answer quickly

Answer 1

Answer:

Step-by-step explanation:

first ,find the zeroes of the quadratic polynomial 2x²-9x + 4.

2x² - 9x + 4 = 0

2x² -8x -x + 4 = 0

2x (x - 4) -1 (x - 4) = 0

(2x - 1) (x - 4) = 0

x = 1/2 or x = 4

As we have given condition, the zeroes of the polynomial x² + px + q

are double in the value to the zeroes Of 2x²-9x + 4

let the zeros of the polynomial

x² + px + q are α and β

α = 2 (1/2) = 1

β = 2 (4) = 8

compare the equation x² + px + q

with standard form of quadratic equation ax² + bx + c = 0

there for, a = 1 , b = p, c = q

we know the relation between coefficients and roots of the quadratic polynomial

α + β =- b/a

(1) + (8) = -p /1

9= -p

p = -9

and (α .β) = c/a

( 1 x 8 ) = q / 1

8 = q

Q=8