Question

If the sum and product of Quadratic polynomial is √2 and -3/2
respectively then one of the Zero is

Answer 1

ANSWER

The zeroes of the polynomial are either -1/√2 and 3/√2 or 3/√2 and -1/√2

GIVEN

• The sum and product of the zeroes of the polynomial is √2 and -3/2

SOLUTION

Let us consider the zeroes of the polynomial be α and β respectively

since sum of the zeroes is √2

⇒ α + β = √2 ..........(1)

and product of the zeroes is -3/2

⇒ αβ = -3/2

⇒α = {-3/(2β)} ...........(2)

Putting the value of α from (2) in (1) we have ,

⇒ {-3/(2β)} + β = √2

⇒ {-3 + 2β²}/2β = √2

⇒ 2β² - 3 = 2√2β = 0

⇒ 2β² - 2√2β - 3 = 0

⇒ 2β² + √2β - 3√2β - 3 = 0

⇒ √2β(√2β + 1) - 3(√2β+1) = 0

⇒(√2β - 3)(√2β + 1) = 0

Therefore ,

⇒ β = 3/√2 or ⇒ β = -1/√2

Now using the value of β in (2)

$\sf \implies \alpha = \dfrac{-3}{2\times \dfrac{3}{\sqrt{2}}} \: \: or \: \: \implies \alpha = \dfrac{-3}{2\times \dfrac{-1}{\sqrt{2}}} \\\\ \sf \implies \alpha = -\dfrac{1}{\sqrt{2}} \: \: or \: \: \implies \alpha = \dfrac{3}{\sqrt{2}}$

Thus , the zeroes of the polynomial are either -1/√2 and 3/√2 or 3/√2 and -1/√2