Question

give an example for quadratic equation.

help me out 9 class questions 1 mask ​

Answer 1

Answer:

y = x^2 + 3x + 1.

this is your answet

Answer 2

In general, a real number $\alpha$ is called a root of the quadratic equation ax²+bx+c=0, if $\alpha \alpha^{2}$ + b$\alpha$+ c = 0. We also say that x = $\alpha$ is a solution of the quadratic equation, or $\alpha$ satisfies the quadratic equation.

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Example :-

$⟶ \: \bf(x + 2)^{3} = {x}^{3} - 4$

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Solution :-

$\sf Here, \\ \sf \: LHS =(x+ 2)^{3} \: \: \: \: \: \: \: = (x+ 2)^{3}(x+ 2)$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (x^{2} + 4x + 4)(x + 2)$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{3} + {2x}^{2} + {4x}^{2} + 8x + 4x + 8$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{3} + 6 {x}^{2} + 12x + 8$

Therefore, $\sf(x + 2)^{3} = {x}^{3} - 4$ can be rewritten as $\bf{x}^{3} + 6 {x}^{2} + 12x + 8 = {x}^{3} - 4$

ie, 6x²+12x+12=0 (or) x²+2x+2=0

It is in the form of ax²+bx+c=0

So, It is a quadratic equation.

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