Question

Find the quadratic polynomial, whose zeroed are in the ratio of 2 : 3 and their sum is 15.

Answer 1

Answer: The required polynomial is $x^2-15x+54=0$

Step-by-step explanation:

Since we have given that

Ratio of zeroes is 2:3.

So, let α = 2x

β = 3x

And their sum would be 15.

so, it becomes,

$2x+3x=15\\\\5x=15\\\\x=\dfrac{15}{5}\\\\x=3$

So, α = 3×2 = 6

β = 3 × 3 =9

So, the quadratic polynomial would be

$x^2-(\alpha +\beta )x+\alpha \beta =0\\\\x^2-(6+9)x+54=0\\\\x^2-15x+54=0$

Hence, the required polynomial is $x^2-15x+54=0$