Question

find a quadratic polynomial whose
sum and product of zeroes are
1/3,-2

Answer 1

$\rule{200}3$

$\color{red}\huge{\underline{\underline{\mathfrak{Question:-}}}}$

Find the quadratic polynomial whose sum and product of zeroes is $\frac{1}{3}$ and -2

$\rule{200}3$

$\color{blue}\huge{\underline{\underline{\mathfrak{Answer}}}}$

$Quadratic polynomial=3x^2-x-6$

$\rule{200}3$

$\color{orange}\huge{\underline{\underline{\mathfrak{Solution:-}}}}$

⠀⠀${\red{\bold{\text{Given:-}}}}$

• Sum of zeroes =$\frac{1}{3}$
• Product of zeroes =-2

${\blue{\bold{\text{We know that}}}}$

Quadratic polynomial =x²-(sum of zeroes}x+(Product of zeroes)

So, According to formula

Quad. polynomial =$x^2-\frac{1}{3}x+\left(-2\right)$

Quad. polynomial =$x^2-\frac{1}{3}x-2$

Quad. polynomial =$\frac{3x^2-x-6}{3}$

$0=3x^2-x-6$

[Because sum of a quadratic polynomial is equal to zero]

$\rule{200}3$

Hope it helps