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Verify relationship 2x²-(1+2√2x)+√2

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Ramesh answered 3 year(s) ago

Find the zeros of the polynomial

Find the zeros of thre polynomial 3√2 x² + 13x + 6√2 and verify the relationship between zeros and coefficients of the polynimial.

Class-X Maths

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Asked by Tonykuttan

Aug 14

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Ramesh , SubjectMatterExpert

Member since Apr 01 2014

Sol:
3√2 x² + 13 x + 6√2
= 3√2 x² + 9x + 4x + 6√2
= 3x(√2 x + 3) + 2√2(√2x + 3)
= (√2x + 3)(3x + 2√2)

Zeroes of the polynomial:
(3x + 2√2) = 0
⇒ x = 2√2/3
(√2x + 3) = 0
⇒ x = -3/√2
Sum of the roots = 2√2/3 -3/√2 = -13/3√2
Product of the roots = 2√2/3 × 3/√2 = 2

Sum of the roots = -b/a = -13/3√2
Product of the roots = c/a = 6√2 / 3√2 = 2.