Question

Find quadratic polynomial whose zeroes are 3 and -2

Answer 1

Answer:

sun of zeros=3+(-2)=3-2=1

product of zeros=3×-2=-6

QUADRATIC EQUATION-

x²-(sum of zeros)x+(product of zeros)=0

-> x²-(1)x+(-6)=0

-> x²-x-6=0

Answer 2

||✪✪ QUESTION ✪✪||

Find quadratic polynomial whose zeroes are 3 and -2 ?

|| ✰✰ ANSWER ✰✰ ||

☙☙ Method ❶ ☙☙ :-

Given that, Roots are (-2) and 3 ...

So,

→ Sum of roots = (-2) + (3 )

→ Sum of roots = 3 - 2

→ Sum of roots = 1

And,

→ Product of roots = (-2) * (3 )

→ Product of roots = (-6)

So,

→ Required equation : x² - ( sum of roots )x + product of roots = 0

= > x² - (1)x + (-6) = 0

= > x² - x - 6 = 0

Hence, Required equation is x² - x - 6 = 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 - 3)( x - (-2)) = 0

= > ( x -3) ( x +2 )

= > x² + 2x -3x - 6 = 0

= > x² - x - 6 = 0.

Hence, Required equation is x² - x - 6 = 0.

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