Question

find a quadratic polynomial whose zeroes are (3,5)​

Answer 1

Step-by-step explanation:

The quadratic polynomial whose zeroes are 3 and -5 is x² + 2x - 15.

Answer 2

ANSWER:

Given:

• Zeroes of polynomial = 3, 5

To Find:

• The quadratic polynomial

Solution:

$\text{\underline{METHOD 1:}}\\\\\text{We are given that, zeroes are 3 and 5. So,}\\\\:\implies x=3\:\:\:and\:\:\:x=5\\\\:\implies x-3=0\:\:\:and\:\:\:x-5=0\\\\\text{Multiplying the equations,}\\\\:\implies(x-3)\times(x-5)=0\times0\\\\:\implies x^2-3x-5x+15=0\\\\\bf{:\implies x^2-8x+15}$

$\\\text{\underline{METHOD 2:}}\\\\\text{We know that,}\\\\:\implies\text{k[x ^2 - (sum of zeroes)x + (product of zeroes)]}\\\\\text{We are given that, zeroes are 3 and 5.}\\\\:\implies k[x^2-(3 + 5)x+(3\times5)]\\\\:\implies k[x^2-8x+15]\\\\\bf{:\implies x^2-8x+15}$