Question

if 2 x square - 7 x + 3 = 0 and 4 x square + a x minus 3 = 0 root are same and equal then find a

Answer 1

$2 {x}^{2} - 7x + 3 = 0$
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$4 {x}^{2} + ax - 3 = 0$
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finding roots of 1st equation..
$2 {x}^{2} - 1x - 6x + 3 = 0 \\ x(2x - 1) - 3(2x - 1) = 0 \\ (x - 3)(2x - 1) = 0 \\ roots \: of \: first \: equation \\ are \: 3 \: and \: \frac{1}{2} ..$
applying the value of x on the second equation.
$4 {x}^{2} + ax - 3 = 0 \\ if \: x = 3 \\ 4 \times {3}^{2} + a \times 3 - 3 = 0 \\ 36 + 3a - 3 = 0 \\ 3a = - 33 \\ a = - 11$
using 2nd root to find the value of a of second equation.
$4 {x}^{2} + ax - 3 = 0 \\ if \: x = \frac{1}{2} \\ 4 \times {( \frac{1}{2} )}^{2} + a \times \frac{1}{2} - 3 = 0 \\ 1 + \frac{a}{2} - 3 = 0 \\ \frac{a}{2} = 2 \\ a = 4$
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