Class 10 Math All topics Quadratic Equations

The following equation is a quadratic equation.

$(x+2)_{3}=x_{3}−4$

(a)

True

(b)

False

Correct answer: (a)

Solution: $(x+2)_{3}=x_{3}−4$

$x_{3}+3(x_{2})(2)+3x(2)_{2}+(2)_{3}=x_{3}−4$

$x_{3}+6x_{2}+12x+8−x_{3}+4=0$

$6x_{2}+12x+12=0$

$6(x_{2}+2x+2)=0$

$⇒$ $x_{2}+2x+2=0$

$⇒$ A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

$⇒$ Comparing equation $x_{2}+2x+2=0$ with standard form of quadratic equation $ax_{2}+bx+c=0$.

$⇒$ We get, $a=1,b=2$ and $c=2$

$∴$ The equation $(x+2)_{3}=x_{3}−4$ is quadratic equation is true.

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introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

surface areas and volumes