Question

if the sum of the quadratic p(x)=(k²-14)x²-2x-4x is 1, then find the value of k. also find zeroes of this polynomial.​

Answer 1

Sum of zeroes = 1

$\to \: \sf{ \alpha + \beta = \cfrac{ - b}{a} }$

Substitute the known values.

$\implies \sf{1 = \dfrac{ - ( - 2)}{ {k}^{2} - 14 } }$

$\implies \sf{1 = \dfrac{2}{ {k}^{2} - 14 } }$

On cross multiplying,

$\implies \sf{ {k}^{2} - 14 = 2 }$

$\implies \sf{ {k}^{2} = 2 + 14 }$

$\implies \sf{ {k}^{2} = 16 }$

$\implies \sf{k = \sqrt{16} }$

$\implies \sf{k = \pm4}$

∴ k = ± 4

KNOW MORE:

• For any Quadratic polynomial, we generally consider it's zeroes as α and β
• Product of zeroes is represented by the formula c ÷ a