Question

If the sum of the zeroes of the quadratic polynomial kx2 +2x+3k is equal to their product, find k

Answer 1

SOLUTION

GIVEN

The sum of the zeroes of the below quadratic polynomial

$\sf{k {x}^{2} + 2x + 3k}$

is equal to their product,

TO DETERMINE

The value of k

EVALUATION

Here the given equation of the quadratic polynomial is

$\sf{k {x}^{2} + 2x + 3k}$

Comparing with the quadratic polynomial

$\sf{a {x}^{2} + bx + c} \: \: we \: get$

a = k , b = 2, c = 3k

Sum of the zeroes

$\displaystyle \sf{ = - \frac{b}{a} }$

$\displaystyle \sf{ = - \frac{2}{k} }$

Product of the Zeroes

$\displaystyle \sf{ = \frac{c}{a} }$

$\displaystyle \sf{ = \frac{3k}{k} }$

$= 3$

Now it is given that, sum of the zeroes of the quadratic polynomial is equal to their product

$\therefore \: \: \displaystyle \sf{ - \frac{2}{k} = 3 }$

$\implies \: \: \displaystyle \sf{ 3k = - 2 }$

$\therefore \: \: \displaystyle \sf{ k = - \frac{2}{3} }$

FINAL ANSWER

The required value is

$\displaystyle \sf{ k = - \frac{2}{3} }$

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Answer 2

Step-by-step explanation:

The sum of the zeroes of the below quadratic polynomial

\sf{k {x}^{2} + 2x + 3k}kx2+2x+3k

is equal to their product,

TO DETERMINE

The value of k

EVALUATION

Here the given equation of the quadratic polynomial is

\sf{k {x}^{2} + 2x + 3k}kx2+2x+3k

Comparing with the quadratic polynomial

\sf{a {x}^{2} + bx + c} \: \: we \: getax2+bx+cweget

a = k , b = 2, c = 3k

Sum of the zeroes

\displaystyle \sf{ = - \frac{b}{a} }=−ab

\displaystyle \sf{ = - \frac{2}{k} }=−k2

Product of the Zeroes

\displaystyle \sf{ = \frac{c}{a} }=ac

\displaystyle \sf{ = \frac{3k}{k} }=k3k

= 3=3

Now it is given that, sum of the zeroes of the quadratic polynomial is equal to their product

\therefore \: \: \displaystyle \sf{ - \frac{2}{k} = 3 }∴−k2=3

\implies \: \: \displaystyle \sf{ 3k = - 2 }⟹3k=−2

\therefore \: \: \displaystyle \sf{ k = - \frac{2}{3} }∴k=−32

FINAL ANSWER

The required value is

\displaystyle \sf{ k = - \frac{2}{3} }k=−32