Question

If sum of the squares of zeroes of the quadratic polynomial 6x2 + x + k is 25/36, the
value of k is:​

Answer 1

Step-by-step explanation:

Given:-

sum of the squares of zeroes of the quadratic polynomial 6x²+ x + k is 25/36

To find:-

Find the value of k?

Solution:-

Given quadratic polynomial= 6x²+x+k

On comparing with the standard quadratic pilynomial ax²+bx+c

we have,

a=6

b=1

c=k

We know that

If α and β are the zeroes of ax²+bx+c then

Sum of the zeroes= α+ β = -b/a

=> α+ β= -1/6 -----(1)

Product of the zeroes =αβ= c/a

=>αβ=k/6 -------(2)

Given that sum of the squares of the zeroes

=25/36

=>α²+ β²= 25/36----(3)

We know that

(a+b)²=a²+2ab+b²

(α+ β)²=α²+ 2αβ+β²

(α+ β)²=(α²+β²)+2αβ

=>(-1/6)²=(25/36)+2(k/6)

=>1/36=(25/36)+(2k/6)

=>(1/36)-(25/36)=2k/6

=>(1-25)/36=k/3

=>-24/36=k/3

=>k/3=-24/36

=>k/3=-2/3

=>k=(-2/3)×3

=>k=-6/3

=>k=-2

Therefore,k=-2

Answer:-

The value of k for the given problem is -2

Used formulae:-

• If α and β are the zeroes of ax²+bx+c then Sum of the zeroes= α+ β = -b/a.
• Product of the zeroes =αβ= c/a
• (a+b)²=a²+2ab+b²
• the standard quadratic pilynomial ax²+bx+c