Question

11. Find a Quadratic polynomial the sum and product of whose zeroes are -5 and 6.​

Answer 1

EXPLANATION.

Quadratic polynomial.

Sum of the zeroes = - 5.

Products of the zeroes = 6.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = - 5. - - - - - (1).

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 6. - - - - - (2).

As we know that,

Formula of the quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-5)x + (6) = 0.

⇒ x² + 5x + 6 = 0.

                                                                                                                       

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Step-by-step explanation:

$\tt \small \leadsto \: \alpha \beta = 6 \\ \alpha + \beta = 5$

Formula Used- x²-(α+ β)x+αβ

Required equation=x²-(-5)x+6=x²+5x+6