Question

Two students Ragini and Gaurav were asked to solve a quadratic equation ax² + bx + c = 0 , a ≠ 0 .
Ragini made some mistakes in writing ' b 'and found the roots as 3 and -1/2 . Gaurav too made mistake in writing ' c ' and found the roots - 1 and -1/4 . The Correct roots of the given equation should be ?

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Answer 1

Final result : x = -2 or 3/4 are the original roots of the quadratic equation :
$a {x}^{2} + bx + c = 0$
Things to know :
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$3)values \: of \: a \: and \: b \: and \: c \: may \\ \: vary \: but \: \: roots \: wi \: always \: be \: constant. \\ \\ \\ \\ \\ \\ \\ \\ hope \: youunderstand \: my \: answer \: and \: it \: may \: helps \: . \\ if \: there \: is \: an \: error \: notify \: me.$

Answer 2

Standard form of Quadratic equation: ax²+bx+c=0

Ragini made some mistakes in writing ' b 'and found the roots as 3 and -½. She made a mistake in the coefficient of x.she write the constant term(c) and the coefficient of x² (a) correct.
Product of zeroes= c/a = 3 ×( -½) = -3/2.

Gaurav too made mistake in writing ' c ' and found the roots - 1 and -1/4 .He made a mistake while writing the constant term (c). He write coefficient of x and x² correct.
Sum of zeroes = -b/a = -1 +(-¼)= -5/4

Quadratic equation : x² - (Sum of zeroes)x + Product of zeroes

x² -(-5/4)x + (-3/2)
x² +5/4x -3/2= 0
4x² +5x -6 = 0
4x² +8x -3x -6 = 0
4x(x +2) -3(x +2) = 0
(4x-3)(x+2) = 0
x = ¾ or x = -2

Hence, the correct roots are -2, 3/4.

HOPE THIS WILL HELP YOU...