Question

If x-2 is a factor of a polynomial kx² - √2x + 1 then find the value of k .

Answer 1

Answer:

x-2=0. x=2

Step-by-step explanation:

now put value of x k*2*2 - root 2 *2 +1. after it solve

Answer 2

Answer:

The value of k is $\tt \dfrac{2\sqrt{2}-1}{4}$

Step-by-step explanation:

Given :

x - 2 is a factor of a polynomial kx² - √2x + 1

To find :

the value of k

Solution :

If (x - a) is a factor of polynomial p(x) , then p(a) = 0

(x - 2) is a factor.

x - 2 = 0

x = +2

Put x = 2,

kx² - √2x + 1 = 0

k(2)² - √2(2) + 1 = 0

4k - 2√2 + 1 = 0

4k = 2√2 - 1

 k = (2√2 - 1)/4

Therefore, the value of k is $\tt \dfrac{2\sqrt{2}-1}{4}$

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About Quadratic Polynomials :  

✯ It is a polynomial of degree 2  

✯ General form :  

  ax² + bx + c  = 0  

✯ Determinant, D = b² - 4ac  

✯ Based on the value of Determinant, we can define the nature of roots.  

D > 0 ; real and unequal roots  

D = 0 ; real and equal roots  

D < 0 ; no real roots i.e., imaginary  

✯ Relationship between zeroes and coefficients :  

 ✩ Sum of zeroes = -b/a  

 ✩ Product of zeroes = c/a  

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