Question

If zeroes of the polynomial x^2+px+q are double in value of zeroes of 2x^2-5x+p. Find p and q.

Answer 1

Answer:

Step-by-step explanation:

Given : 2x² - 5x - 3

2x² - 6x +1x - 3 = 0

[By middle term splitting ]

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

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

x -3 = 0 or 2x+1 = 0

x = 3, x = -1/2

Two zeroes are 3 & -1/2

zeroes of x² +px+q are 2×3 = 6 and 2 × -1/2 = -1

[ Given zeroes are double]

Let the two zeroes be α = 6 and β  = -1 of Polynomial x² +px+q

On comparing with ax²+bx+c

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

Sum of zeroes (α+ β) = -b/a

6 +( -1) = -p/1

6 -1 = -p

5 = - p

p = -5

Product of zeroes (α. β) = c/a

6 × -1 = q/1

-6 = q

q = -6

Hence, the value of p & q is -5 & -6.

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