Question

if the zeroes of the polynomial x^2+px+q are double in value to the zeroes of 2x^2-5x-3 find p and q

Answer 1

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.
HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let f(x) = 2x² - 5x - 3

and the zeros of polynomial be α and β, then

Sum of zeros = α + β = 5/2

Product of zeros = αβ = - 3/2

According to the Question,

Zeros of x² + px + q are 2α and 2β

Sum of zeros = - Coefficient of x/Coefficient of x² = - p/1

⇒ - p = 2α + 2β = 2 (α + β)

⇒ - p = 2 × 5/2 = 5

⇒ p = - 5

Product of zeros = Constant term/Coefficient of x² = q/1

⇒ q = 2α × 2β = 4 αβ

⇒ q = 4 (- 3/2) = - 6

Hence, the values of p and q are - 5 and - 6.