Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients
(a) 3x²-x-4
in splitting method. with steps​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Step-by-step explanation:

$Let, \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: the \: quadratic \: polynomial</p><p>.$

$3 {x}^{2} - x - 4 = 0$

$3 {x}^{2} - 4x + 3x - 4 = 0$

$x(3x - 4) + 1(3x - 4) = 0$

$(x + 1)(3x - 4) = 0$

$x = - 1, x = \frac{4}{3}$

$Sum \: of \: zeroes = \frac{ - b}{a}$

$\implies \frac{ 1}{3}$

$Product \: of \: its \: zeroes = \frac{c}{a}$

$\implies \frac{ - 4}{3}$

${x}^{2} - ( \alpha + \beta )x + ( \alpha \times \beta ) = 0$

${x}^{2} - \frac{1}{3} x - \frac{4}{3}$

$3 {x}^{2} - x - 4 = 0$

Hence verified