Find the zeroes of the following quadratic polynomials and verify the relationships between the zeros abd the coefficiants. (1) 2x^2+6-8x
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Answer:-
Given Polynomial => 2x² - 8x + 6 = 0
By splitting the middle term,
2x² - 2x - 6x + 6 = 0
→ 2x ( x - 1) - 6 ( x - 1) = 0
→ (2x - 6)( x - 1) = 0
2x - 6 = 0
→ 2x = 6
→ x = 6/2
→ x = 3
x - 1 = 0
→ x = 1
Verification:-
Let , a = 2 ; b = - 8 ; c = 6 .
We know that,
Sum of the roots = - b/a.
→ 3 + 1 = -(-8)/2
→ 4 = 8/2
→ 4 = 4
Product of the roots = c /a
→ (3)(1) = 6/2
→ 3 = 3
Hence, Verified.
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