Question

Find a quadratic equation whose zeroes r 3and -3

Answer 1

Step-by-step explanation:

given :-

the zeroes of a quadratic equation is 3 and -3

to find :-

the quadratic equation

SOLUTION :-

let the quadratic equation has variable X

so according to question

X=3 or -3

=>X-3=0 or X+3=0

so X-3 and X+3 both are factors of the quadratic equation

and we know that a quadratic equation can have maximum 2 factors

so the quadratic equation is given by multiplying both the factors

so required equation :-

so required equation :-(X-3)(X+3)

so required equation :-(X-3)(X+3)we know that

so required equation :-(X-3)(X+3)we know that(X-Y)(X+Y)=X²-Y²

so required equation :-(X-3)(X+3)we know that(X-Y)(X+Y)=X²-Y²so it will be :-

so required equation :-(X-3)(X+3)we know that(X-Y)(X+Y)=X²-Y²so it will be :-X²-9

more questions rearding the topic

Q. WHAT IS A QUADRATIC EQUATION ?

=>the equation which have maximum power of variable as 2

Q.HOW TO SOLVE QUADRATIC EQUATION

=>we have a variety of method to solve a quadratic equation such as

• quadratic formula
• factorisation method
• completing the square method

Answer 2

$\mathfrak{Question}\\ \texttt {Find a quadratic equation whose zeroes are 3 and -3}$

$\rm A\ polynomial\ is\ of\ the\ form\ ax^2-bx+c\\ \rm Given\ that\ the\ zeroes\ are\ 3\ and\ -3.\\ \rm We\ know,\ sum\ of\ zeroes\ is\ given\ by\ \frac{-b}{a}\\ \\ \rm and\ product\ of zeroes\ is\ given\ by\ \frac{c}{a}\\ \\ \rm And\ you\ should\ know\ that,\ if\ we\ know\ the\ zeroes\ of\ the\ polynomial,\ we\ can\ form\ the\ polynomial.\\ \rm x^2-(sum\ of\ zeores)+(product\ of\ zeroes)\\ \rm Now,\ the\ zeroes\ are\ 3\ and\ -3,\ so\ sum\ of\ zeores\ = 3+(-3)=0\: \; Product\ of\ zeroes\ = 3\times-3=-9\\ \\ \rm Putting\ values\ in\ the\ equation,\ The\ polynomial\ will\ be\ x^2-0x+(-9)\\ \implies \therefore x^2-9=0\ is\ the\ polynomial.$

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Value of x

$x^2-9=0\\ \implies x^2=9\\ \implies x=\sqrt9\\ \therefore x=3 and -3\\ \bf{Hence\ Verified}$