Question

2.Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively:. (i) 2/3 -4 (ii) -1/sqrt(2) 1/sqrt(2) (iii) sqrt(5) -2 (iv) -1/sqrt(2) 2/3​

Answer 1

Solution

Given :-

• Sum and product of roots are (1). 2/3 , -4 (2) -1/√2 , 1/√2 (3). √5 , -2

Find :-

• Polynomial equation

Explanation

Using Formula

$\boxed{\underline{\tt{\red{\:x^2-(Sum\:of\:roots)x\:+(Product\:of\:roots)\:=\:0}}}}$

Case 1.

When,

• Sum of roots = 2/3
• Product of roots = -4

Equation will be

==> x² - (2/3 )x + (-4) = 0

==> x² - 2x/3 - 4 = 0

==> 3x² + 2x - 12 = 0 [ Ans ] .

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Case 2.

When,

• Sum of roots = -1/√2
• Product of roots = 1/√2

Equation will be

==> x² - ( -1/√2 )x + (1/√2) = 0

==> x² + x/√2 - 1/√2 = 0

==> √2x² + x - 1 = 0 [ Ans.]

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Case 3.

When

• Sum of roots = √5
• Product of roots = -2

Equation will be

==> x² - ( √5 )x + (-2) = 0

==> x² - √5 x - 2 = 0 [ Ans].

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Case 4.

When

• Sum of roots = -1/√2
• Product of roots = 2/3

Equation will be

==> x² - (-1/√2 )x + (2/3) = 0

==> x² + x/√2 + 2/3 = 0

==> 3√2 x² +3x + 2√2 = 0 [ Ans].

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