1.

Determine whether the given quadratic equations have real roots ,if so find the roots 6x^2+x-2= 0​

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Step by step SOLUTION:

Given \ p(x)=6x^{2}+x-2\\\\we \ have \ to \ check \ whether \ p(x) \ have \ real \ roots \ or \ not.\\\\For \ real \ roots =b^{2}-4ac\geq0\\\\putting \ value \ here\\\\b^{2}-4ac\geq0\\\\ 1^{2}-(4 \times6 \times-2)=1+24=25\\\\ b^{2}-4ac\geq0 \ so \ p(x) \ has \ real \ roots\\\\p(x)=6x^{2}+x-2\\\\p(x)=6x^{2}+4x-3x-2\\\\p(x)=2x(3x+2)-(3x+2)\\\\p(x)=(3x+2)(2x-1)\\\\\alpha =3x+2=0 \ or \ \beta =2x-1\\\\x=\frac{-2}{3} \ or \ x=\frac{1}{2}

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