31. One zero of the polynomial x2 - 2x - (7p + 3), find the value of p

1.	31. One zero of the polynomial x2 - 2x - (7p + 3), find the value of p and the other(C.B.S.E. 2012)Chili11. 3
Answer» Given f(x) = x^2 – 2 x – (7 p + 3) Given one zero of polynomial f(x) = - 4 and other zero be a So sum of zeroes = coefficient of x / coefficient of x^2 -4 + a = - (- 2)/1 -4 + a = 2 a = 2 + 4 = 6 The other zero is 6 Now product of zeroes = constant term / coefficient of x^2 -4 x 6 = - (7 p + 3) / 1 -24 = - (7 p + 3) 7 p + 3 = 24 7 p = 24 – 3 7 p = 21 P = 3 So the value of p is 3 x²-2x-(7p+3) = 0 (-4)²-2(-4)-7p-3 = 0 16+8-3-7p = 0 21-7p = 0 -7p = -21 p = 21/7 p = 3 If p = 3 , then (-4) is a factor of p(x)

31. One zero of the polynomial x2 - 2x - (7p + 3), find the value of p and the other(C.B.S.E. 2012)Chili11. 3

Answer»

Given f(x) = x^2 – 2 x – (7 p + 3)

Given one zero of polynomial f(x) = - 4 and other zero be a

So sum of zeroes = coefficient of x / coefficient of x^2

-4 + a = - (- 2)/1

-4 + a = 2

a = 2 + 4 = 6

The other zero is 6

Now product of zeroes = constant term / coefficient of x^2

-4 x 6 = - (7 p + 3) / 1

-24 = - (7 p + 3)

7 p + 3 = 24

7 p = 24 – 3

7 p = 21

P = 3

So the value of p is 3

x²-2x-(7p+3) = 0

(-4)²-2(-4)-7p-3 = 0

16+8-3-7p = 0

21-7p = 0

-7p = -21

p = 21/7

p = 3

If p = 3 , then (-4) is a factor of p(x)