Question

if one zero of a quadratic polynomial ( k - 1) X
square + kx + 1 is minus 3 then value of k is​

Answer 1

Question:

If one zero of the quadratic polynomial

( k - 1 )x^2 + kx + 1 is -3 then find the value of k .

Answer:

k = 4/3

Note:

If x = a is a zero of the given polynomial p(x) ,

then , at x = a the value of polynomial p(x) will become zero. ie; p(a) = 0.

Solution:

Let the given polynomial be;

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

It is given that ,

-3 is a zero of the given polynomial.

Thus, at x = -3 , p(x) will become zero.

ie,

=> p(-3) = 0

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

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

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

=> 6k - 8 = 0

=> 6k = 8

=> k = 8/6

=> k = 4/3

Hence,

The required value of k is 4/3.

Answer 2

$\Huge{\underline{\underline{\red{\sf{Question :}}}}}$

If one zero of a quadratic polynomial ( k - 1) x square + kx + 1 is minus 3 then value of k is ?

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$\Huge{\underline{\underline{\red{\sf{Answer :}}}}}$

We have equation :

(k - 1)x² + kx + 1 = 0

If one of zero of polynomial is -3

Put x = -3

⇒(k - 1)(-3)² + (-3)k + 1 = 0

⇒(k - 1)9 -3k + 1 = 0

⇒9k - 9 -3k + 1 = 0

⇒6k - 9 + 1 = 0

⇒6k - 8 = 0

⇒6k = 8

⇒k = 8/6

⇒k = 4/3

$\Large{\underline{\boxed{\red{\sf{k \: = \: \frac{4}{3}}}}}}$

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For finding other zero.

put k = 4/3 in equation,

⇒ (4/3 - 1)x² + (4/3)x + 1 = 0

⇒[(4 - 3)/3]x² + 4/3x + 1 = 0

⇒1/3x² + 4/3x + 1 = 0

⇒1/3x² + 1/3x + 3/3x + 1 = 0

⇒1/3x² + 1/3x + 1x + 1 = 0

⇒1/3x(x + 1) + 1(x + 1) = 0

⇒(1/3x + 1) (x + 1) = 0

Other zeros

x = -3 , -1

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