Question

Which of the following is a quadratic equation? l

A) x^2+x^3=2

B) p(p-3)=0

C) x^2=6+x^2-x

D) x^2 +1/x= 5

​

Answer 1

${\huge{\pink{\underline{\underline{\purple{\mathbb{\bold{\mathcal{AnSwEr..}}}}}}}}}$

${\large{\blue{\bold{\underline{We\:Know\:That:-}}}}}$

▪︎ Standard form of a quadratic equation,

= ax²+bx+c = 0.

${\large{\blue{\bold{\underline{Now,}}}}}$

A)

$\implies \: {x}^{2} + {x}^{3} = 2 \\ \\ \implies \: {x}^{3} + {x}^{2} - 2 = 0$

Hence it is not a quadratic equation.

B)

$\implies \: p(p - 3) = 0 \\ \\ \implies \: {p}^{2} - 3p - 0 =0$

Hence it is a quadratic equation.

C)

$\implies \: x {}^{2} = 6 + {x}^{2} - x \\ \\ \implies x - 6 = 0 \\ \\ \implies \: 0{x}^{2} + x - 6 = 0$

Hence it is a quadratic equation.

D)

$\implies{x}^{2} + \frac{1}{x} = 5 \\ \\ \implies \: x {}^{3} + 1 = 5x \\ \\ \implies \: {x}^{3} - 5x + 1 = 0$

Hence it is not a quadratic equation.