Question

find a quadratic polynomial each with given as sum and product 2, 3

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{x^2\:-\:3x\:+\:2\:=\:0}}\:\:\star\:\bf{is\:the\:Required\:Polynomial\:.}}$

Correct Question :–

Find a quadratic polynomial each with given sum and product as 3 and 2 .

Explanation :

Given :–

• Sum of roots of a Quadratic Polynomial is 3 .

• Products of roots of a Quadratic Polynomial is 2 .

To Find :–

• The Quadratic Polynomial whose sum of roots and product of are 3 and 2 respectively .

Solution :–

☆ Skeletal Quadratic Equation is :-

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

We have , Product of roots = 2 and Sum of roots = 3 .

★ Putting these values in the Skeletal Quadratic Equation :-

⇒ x² - (3)x + (2) = 0

⇒ x² - 3x + 2 = 0

∴ The Required polynomial is x² - 3x + 2 = 0 .

$\dag$ Additional Information :–

 Let ax² + bx + c = 0 is a Quadratic Polynomial then :

• $\sf{Sum\:of\:Roots\:=\:-\dfrac{b}{a} }$

• $\sf{Product\:of\:Roots\:=\:\dfrac{c}{a} }$

Answer 2

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ Find a quadratic polynomial each with given as sum and product 2, 3 ?

$\mathtt{\huge{\underline{\green{AnSwEr:-}}}}$

✏ The polynomial is x² - 3x -2 = 0 satisfy the question.

$\mathtt{\huge{\underline{\pink{Solution:-}}}}$

Given :–

• The sum of roots of a quad.polynomial is 3 .

• The products of roots of a quad.polynomial is 2 .

To Find :–

A quad. polynomial whose roots sum is 3 and roots product are 2 .

Calculation :–

We know,

➡ x² - (sum of roots)x + (product of roots) = 0....(1)

Where ,

• The product of roots is 2 .

• The Sum of roots is 3 .

Putting value in equation (1)

⇒ x² - (3)x + (2) = 0

⇒ x² - 3x + 2 = 0

∴ The polynomial is x² - 3x + 2 = 0.

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✅ Verification :-

Let ax² + bx + c = 0 is a Quadratic Polynomial then :

• Sum of Roots = -b/a = -(-3)/1 = 3

The sum of roots of a quad.polynomial is 3 .(Given)

• Product of roots = c/a = 2/1 = 2

The product of roots is 2 .(Given)

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