Question

If one zero of the polynomial x2

-6x+q is twice of the other, find the value of q​

Answer 1

Answer:

q=8.

Step-by-step explanation:

Let the roots of the equation x²-6x+q=0 be x and 2x.

⇒Sum of the roots x+2x=3x=-(-6)/1

⇒3x=6

⇒x=2.

⇒Product of the roots x(2x)=q/1

⇒2x²=q

⇒2(2²)=q

⇒q=8.

Answer 2

Given:

$x^2-6x+q$

To find:

q=?

Solution:

$x^2-6x+q$

if α and β are the roots of the polynomial. as per situation α = 2β

compare the given value:

$\to ax^2+bx+c=0\\\to a= 1\\\to b=-6\\\to c=q$

Formula:

$\to \alpha +\beta= -\frac{b}{a}\\\\\to \alpha\beta= \frac{c}{a}$

$\to 2 \beta+\beta= \frac{6}{1}\\\\\to 3 \beta= 6\\\\\to \beta= 2\\\\\to 2\beta \times \beta= \frac{q}{1}\\\\\to 2\beta^2 = q\\\\\to 2\times 2^2=q\\\\\to q= 2\times 4\\\\\to q= 8$

The final value of q is 8.