Question

if alfa and Bita are the zero of the polynomial f of x = x² - 6x + k. find the value of k such that alfa² + bita² = 40.

Answer 1

Step-by-step explanation:

If alpha and beta are zeros of polynomial f(x)=x2-6x+k find value of k such that alpha2 +beta2 =40

2

Answer 2

k=-2

Step-by-step explanation:

The given equation is:

$</p><p>x^{2}-6x+kx </p><p>2</p><p> −6x+k , comparing this equation with ax^{2}+bx+c=0ax </p><p>2</p><p> +bx+c=0 , we have a=1, b=-6, c=k.</p><p></p><p>Now, if α and β arethe two zeroes of the given polynomial, then α+β=\frac{-b}{a}=6 </p><p>a</p><p>−b</p><p> </p><p> =6 and αβ=\frac{c}{a} </p><p>a</p><p>c</p><p> </p><p> =kk</p><p></p><p>Also, it is given that {\alpha}^{2}+{\beta}^{2}=40α </p><p>2</p><p> +β </p><p>2</p><p> =40</p><p></p><p>⇒{\alpha}^{2}+{\beta}^{2}=({\alpha}+{\beta})^{2}-2{\alpha}{\beta}α </p><p>2</p><p> +β </p><p>2</p><p> =(α+β) </p><p>2</p><p> −2αβ</p><p></p><p>⇒40=(6)^{2}-2k40=(6) </p><p>2</p><p> −2k</p><p></p><p>⇒40-36=-2k40−36=−2k</p><p></p><p>⇒k=-2k=−2$