Question

the roots are 10 & -10 find an equation​

Answer 1

Correct Question :-

• Find The Quadratic Equation whose two Roots are 10 and (-10) ?

Solution :-

☙☙ Method ❶ ☙☙ :-

Given that, Roots are 10 and (-10) ...

So,

→ Sum of roots = 10 + ( - 10 )

→ Sum of roots = 10 - 10

→ Sum of roots = 0

And,

→ Product of roots = 10 * ( - 10 )

→ Product of roots = (-100)

So,

→ Required equation : x^2 - ( sum of roots )x + product of roots = 0

= > x² - 0x + (-100) = 0

= > x² - 100 = 0

Hence, Required equation is x² - 100 = 0.

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☙☙ Method ❷☙☙ :-

We know, Any quadratic equation can also be written in this form : ( x - a )( x - b ) = 0, where a and b are the roots of the equation.

Thus, here,

= > ( x - 10 )( x - (-10)) = 0

= > ( x - 10) ( x + 10) = 0

= > x² + 10x -10x - 100 = 0

= > x² - 100 = 0

Hence, Required equation is x² - 100 = 0.

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Answer 2

Correct Question :-

Find The Quadratic Equation whose two Roots are 10 and (-10) ?

Solution :-

Roots are 10 and (-10 ).

=> Sum of roots = 10 + ( - 10 )

=> Sum of roots = 10 - 10

=> Sum of roots = 0

=> Product of roots = 10 * ( - 10 )

=> Product of roots = (-100)

So,

Required equation : x^2 - ( sum of roots )x + product of roots = 0

=> x² - 0x + (-100) = 0

=> x² - 100 = 0

.°. Required equation is x² - 100 = 0.

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