Question

For quadratic polynomial P(x) = x2

+ (k - 9)x + (k - 1), if the sum

of its zeroes and the product of its zeroes are equal then k = ______​

Answer 1

Answer:

CORRECT QUESTION:-

If sum and products of the roots of the given polynomial p(x)=x²+(k-7)x+k+1 are equal then find the value of k

GIVEN:-

p(x)=x²+(k-7)x+k+1 and product and sum of the roots are equal

TO FIND:-

The value of k

EXPLANATION:-

\underline{\underline{\bf SUM \: OF \: ROOTS:-}}

SUMOFROOTS:−

We know that

\boxed{\sf sum \: of \: roots =\dfrac{-coefficeint \: of \: x }{coefficient \: of \: x^2}=\dfrac{-b}{a}}

sumofroots=

coefficientofx

2

−coefficeintofx

=

a

−b

here from the polynomial

b=(k-7)

a=1

c=k+1

Substituting

sum of roots =-(k-7)/1

\underline{\underline{\bf PRODUCT \: OF \: ROOTS:-}}

PRODUCTOFROOTS:−

\boxed{\sf product \: of \: roots =\dfrac{constant \: term }{coefficient \: of \: x^2}=\dfrac{c}{a}}

productofroots=

coefficientofx

2

constantterm

=

a

c

Substituting

product of roots =k+1/1

Given

sum of roots=product of roots

=>-(k-7)=k+1

=>-k+7=k+1

=>2k=6

\boxed{\sf k=3}

k=3