Question

if a and b are the zeros of the quadratic polynomial f(x)=x2+10x + k such that a-b = 6 then find the value of k​

Answer 1

ANSWER-

Answer

AnswerSince a and b are the zeros of the polynomial f(x)=x

AnswerSince a and b are the zeros of the polynomial f(x)=x 2

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+k

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots =

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = p

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=k

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=kNow, a−b=1

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=kNow, a−b=1(a−b)

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=kNow, a−b=1(a−b) 2

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=kNow, a−b=1(a−b) 2 =1

AnswerSince a and b are the zeros of the polynomial f(x)=x 2 −5x+kThe standard quadratic equation is px 2 +qx+r=0 Then Sum of roots = − pq and Product of roots = pr Therefore,a+b=5 and ab=kNow, a−b=1(a−b) 2 =1(a+b)

.

Answer 2

Answer:

Answer:

k=-2

Step-by-step explanation:

The given equation is:

x^{2}-6x+kx

2

−6x+k , comparing this equation with ax^{2}+bx+c=0ax

2

+bx+c=0 , we have a=1, b=-6, c=k.

Now, if α and β arethe two zeroes of the given polynomial, then α+β=\frac{-b}{a}=6

a

−b

=6 and αβ=\frac{c}{a}

a

c

=kk

Also, it is given that {\alpha}^{2}+{\beta}^{2}=40α

2

+β

2

=40

⇒{\alpha}^{2}+{\beta}^{2}=({\alpha}+{\beta})^{2}-2{\alpha}{\beta}α

2

+β

2

=(α+β)

2

−2αβ

⇒40=(6)^{2}-2k40=(6)

2

−2k

⇒40-36=-2k40−36=−2k

⇒k=-2k=−2