Question

5. Find the zeroes of polynomial 2x^2 + 5x - 12 and verify the relationship between its zeroes and its coefficients.

Class 10

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Answer 1

Let Alpha = -4 and beta = 3/2



Relationship between the zeroes and Coefficient.


Sum of zeroes = Alpha + Beta = -4 + 3/2 = -8+3/2 = -5/2 = - ( Coefficient to X )/ Coefficient to X².



And,


Product of zeroes = -4 × 3/2 = -12/2 = Constant term / Coefficient to X².



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Answer 2

$2x ^{2} + 5x - 12 = 0 \\ 2 {x}^{2} + 8x - 3x - 12 = 0 \\ 2x(x + 4) - 3(x + 4) = 0 \\ (2x - 3)(x + 4) = 0 \\ 2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} \\ and \\ x + 4 = 0 \\ x = - 4 \\ the \: zeroes \: of \: \: quadratic \: polynomial \: are \: \frac{3}{2} \: and \: - 4 \\ sum \: of \: zereos = \frac{3}{2} + ( - 4) = \frac{ - 5}{2} = - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} } \\ product \: of \: zeroes = \frac{3}{2} \times( - 4) = - 6 = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$