Question

If one zero of the polynomial p(x)=x2-6x+k is twice the other then find the value of k​

Answer 1

Answer:

k = 8

Step-by-step explanation:

If f(x) = ax² + bx + c , the relationship between zeros of f(x) and its coefficients are

$x_{1}$ + $x_{2}$ = - $\frac{b}{a}$ and $x_{1}$ × $x_{2}$ = $\frac{c}{a}$

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Let α and β be the zeros of given function and α = 2β, then

α + α/2 = 6 ⇒ 3α = 12 ⇒ α = 4  

β = 2  

α × β = k ⇒ k = 8