Question

if the sum of the zeros of the quadratic polynomial k x² - 3 x + 5 is 1 then find the value of k




please answer ​

Answer 1

Step-by-step explanation:

k(1)²-3(1)+5, x=1

K-3+5=0

k+2=0

k= -2

Answer 2

Answer:

The value of k for which the sum of the zeroes of the quadratic polynomial kx² - 3x + 5 is 1 = 3

Step-by-step explanation:

Given :

the sum of the zeros of the quadratic polynomial kx² - 3x + 5 is 1

To find :

the value of k

Solution :

The given quadratic equation is kx² - 3x + 5

• x² coefficient = k

• x coefficient = -3

• constant term = 5

we know that,

For the quadratic equation ax² + bx + c = 0 , if α and β are zeroes of the polynomial

Sum of zeroes = -b/a

α + β = -b/a

Therefore,

The relation between sum of zeroes and coefficients is,

$\sf Sum \ of \ zeroes =\dfrac{-(x \ coefficient)}{x^2 \ coefficient}$

⇒ 1 = -(-3)/k

⇒ 1 = 3/k

⇒ k = 3

∴ The value of k is 3

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Also,

The other relation between zeroes and coefficients is,

 $\sf Product \ of \ zeroes=\dfrac{constant \ term}{x^2 \ coefficient}$

i.e., For the quadratic equation ax² + bx + c = 0 , if α and β are zeroes of the polynomial

    αβ = c/a