Question

Find the roots of the quadratic equation 2x^2-5x-7 =0 and verify the relationship between their coefficient and routes

Answer 1

Polynomial = 2x^2 - 5x - 7 = 0

Factorising :-

2x^2 + 2x - 7x - 7 = 0

2x(x + 1) - 7(x + 1) = 0

(x + 1)(2x - 7) = 0

(x + 1) = 0

x = -1

(2x - 7) = 0

2x = 7

x = 7/2

- Roots of equation are -1 and 7/2.

Verifying relation between coefficients and roots :-

Sum of zeroes = -1 + 7/2 = 5/2

Product of zeroes = -1 x 7/2 = -7/2

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Answer 2

Step-by-step explanation:

Factorisation:

$\implies \: {2x}^{2} - 5x - 7 = 0$

$\implies \: {2x}^{2} + 2x - 7x - 7$

$\implies \: 2x(x + 1) - 7(x + 1)$

$\implies(2x - 7)(x + 1)$

now,

$2x - 7 = 0 \\ 2x = 7 \\ x = \frac{7}{2} (or) \alpha = \frac{7}{2}$

and,

$x + 1 = 0 \\ x = - 1(or) \beta = - 1$

VerifiCatioN:

$\alpha + \beta = \frac{7}{2} - 1 = \frac{5}{2}$

we know that

$\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 5)}{2} = \frac{5}{2}$

and,

$\alpha \beta = \frac{7}{2 } \times ( - 1) = \frac{ - 7}{2}$

we know that

$\alpha \beta = \frac{c}{a} = \frac{ - 7}{2}$