Question

if x=1/2 and x=-2 are roots of equation (p+1)x²-3x-q=0, then find the value of p+q+5​

Answer 1

Answer:

-1. x=1/2 .x= -2 answer o

Answer 2

Given:-

• f(x) = (p + 1)x² - 3x - q = 0
• x = 1/2, and x = -2 are the roots of f(x)

To find:-

• The value of p + q + 5

Answer:-

If x = a is a root of f(x), that means the value of f(x) is equal to 0 at x = a, that is f(a) = 0.

It is given that, x = 1/2 and x = -2 are the roots of f(x).

So, f(1/2) = f(-2) = 0

f(1/2):

f(1/2) = (p + 1){(1/2)²} - 3(1/2) - q = 0

→ (p + 1)(1/4) - 3/2 - q = 0

Multiplying L.H.S. and R.H.S. by 4,

→ 4{(p + 1)(1/4)} - 4(3/2) - 4q = 0

→ (p + 1) - 6 - 4q = 0

→ p + 1 - 6 - 4q = 0

→ p - 4q = 5 ...(1)

f(-2):

f(-2) = (p + 1)(-2²) - 3(-2) - q = 0

→ 4(p + 1) + 6 - q = 0

→ 4p + 4 + 6 - q = 0

→ 4p - q = -10

Multiplying L.H.S. and R.H.S. by 4,

→ 16p - 4q = -40 ...(2)

Subtracting (2) from (1),

p - 4q - (16p - 4q) = 5 - (-40)

→ p - 4q - 16p + 4q = 45

→ -15p = 45

→ p = -3 ...(3)

From (1) and (3),

p - 4q = 5

→ -3 - 4q = 5

→ -8 = 4q

→ q = -2

So,

p + q + 5 = -3 - 2 + 5

→ p + q + 5 = 0 Ans.