Question

Find the value of k so that the sum of the zeros of the quadratic polynomial is
equal to the product of the zeros of the polynomial (k+1)x²+2kx+4​

Answer 1

EXPLANATION.

Quadratic polynomial.

⇒ (k + 1)x² + 2kx + 4.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -(2k)/(k + 1).

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 4/k + 1.

To find :

Sum of zeroes of quadratic equation = products of zeroes of quadratic equation.

⇒ α + β = αβ.

⇒ -(2k)/k + 1 = 4/k + 1.

⇒ - 2k = 4.

⇒ - k = 2.

⇒ k = -2.

                                                                                                                     

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

Solution

Sum of the zeroes is given by

$\bf \alpha + \beta = \dfrac{-b}{a}$

Product of zeroes is given by

$\bf\alpha\beta = \dfrac{c}{a}$

We have

$\begin{cases}\bf a = k + 1\\ \bf b = -2k \\ \bf c = 4\end{cases}$

By putting value

$\sf \dfrac{-2k}{k+1} = \dfrac{4 }{k+1}$

$\sf -2k = 4$

$\sf - k =\dfrac{4}{2}$

$\sf -k = 2$

$\sf k = -2$