Question

if alpha and beta are the zeros of the polynomial x^2-16,then alpha×beta(alpha + beta)​

Answer 1

Answer:

f(x)=x2−x−k=0

α+β=1αβ=−k

α−β=9αβ=−k

α=55(−4)=−k

β=−4k=20

∴k=20

Step-by-step explanation:

f(x)=x2−x−k=0

α+β=1αβ=−k

α−β=9αβ=−k

α=55(−4)=−k

β=−4k=20

∴k=20

Answer 2

EXPLANATION.

α and β are the zeroes of the polynomial.

⇒ x² - 16.

As we know that,

Quadratic equation written in the form of : ax² + bx + c.

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = 0.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = (-16)/1. = - 16.

To find : αβ(α + β).

Put the values in the equation, we get.

⇒ αβ(α + β) = (- 16)(0).

⇒ αβ(α + β) = 0.

                                                                                                                   

MORE INFORMATION.

D = Discriminant.

D = b² - 4ac.

(1) If D < 0.

One roots = α + iβ.

Other roots α - iβ.

(2) If D > 0.

One roots = α + √β.

Other roots = α - √β.