Question

if the sum of the zeroes of the quadratic polynomial
p(x) = kx² - 3x + 5 is 1 , find the value of k​

Answer 1

Answer :

k = 3

Note :

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

Solution :

Here ,

The given quadratic polynomial is ;

kx² - 3x + 5 .

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we have ;

a = k

b = -3

c = 5

Also ,

It is given that , the sum of zeros of the given quadratic polynomial is 1 .

=> Sum of zeros = 1

=> -b/a = 1

=> -(-3)/k = 1

=> 3/k = 1

=> 3 = k

=> k = 3

Hence , k = 3 .

Answer 2

Step-by-step explanation:

Given:

Sum of zeros of polynomial is kx2 – 3x + 5 is 1. We know that,

Sum of zeros = -(coefficient of x)/(coefficient of x2)

= -(-3) / k = 3/k

From above results,

we get

3/k = 1 Or k = 3

hope it helps

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