Question

if one of the zeroes of the quadratic polynomial (k-1)^2 + kx +1 is -3, then find the value of k.

Answer 1

Step-by-step explanation:

Given Question:-

If one of the zeroes of the quadratic polynomial (k-1)^2 + kx +1 is -3, then find the value of k.

Correction:-

The quadratic polynomial (k-1)x^2 + kx +1

To find:-

Find the value of k ?

Solution:-

Method -1:-

Given quardratic polynomial is

p(x) = (k-1)x^2 + kx +1

Given zero = -3

We know that

If -3 is zero of the quardratic polynomial then it satisfies the given polynomial.i.e. p(-3) = 0

=> (k-1)(-3)^2+k(-3)+1 = 0

=> (k-1)(9)-3k+1 = 0

=> 9k-9-3k+1 = 0

=> (9k-3k) +(-9+1) = 0

=> 6k -8 = 0

=> 6k = 8

=> k = 8/6

=> k = 4/3

Therefore, k = 4/3

Method-2:-

One of the zeroes = -3

Let the other zero be X

Given Polynomial is (k-1)x^2 + kx +1

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = k-1

b= k

c= 1

we know that

sum of the zeroes = -b/a

=> -3+X = -k/(k-1)

=> X = 3 - [k/(k-1)]

=> X = [3(k-1)-k]/(k-1)

=>X = (3k-3-k)/(k-1)

=>X = (2k-3)/(k-1)------(1/

Product of the zeores = c/a

=> (-3)X = 1/(k-1)

=> -3X = 1/(k-1)

from (1)

=> -3[(2k-3)/(k-1)] = 1/(k-1)

=> -3(2k-3) = 1

=> -6k+9 = 1

=> -6k = 1-9

=> -6k = -8

=>6k = 8

=> k = 8/6

=> k = 4/3

Answer:-

The value of k for the given problem is 4/3

Used Concept:-

If k is a zero of the Polynomial p(x) then it satisfies the given Polynomial .i.e.P(k) = 0

Used formulae:-

• the standard quadratic Polynomial is ax^2+bx+c

• sum of the zeroes = -b/a

• Product of the zeores = c/a