From quadratic equation whose roots are 3/4and -2/3

1.	From quadratic equation whose roots are 3/4and -2/3
Answer» ong>GIVEN :- roots of quadratic EQUATION are 3/4 and -2/3. TO FIND :- The quadratic equation by the GIVEN roots SOLUTION :- As we KNOW that the quadratic equation is given by, $\\ : \implies \displaystyle \sf \:x^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0\\ \\$ α = 3/4. β = -2/3 Now, by SUBSTITUTING the values we get, $\\ : \implies \displaystyle \sf \:x^{2} - \bigg( \frac{3}{4} - \frac{2}{3} \bigg)x + \bigg( \frac{3}{4} \times \frac{ - 2}{3} \bigg)= 0 \\ \\ \\$ $: \implies \displaystyle \sf \:x^{2} - \bigg( \frac{9 - 8}{12} \bigg)x + \bigg( \frac{ - 2}{4} \bigg) = 0 \\ \\ \\$ $: \implies \displaystyle \sf \:x^{2} - \frac{1}{12} x + \bigg( \frac{ - 1}{2} \bigg) = 0 \\ \\ \\$ $: \implies \underline{ \boxed{ \displaystyle \sf \bold{ \:x^{2} - \frac{1}{12} x - \frac{1}{2} = 0}}} \\ \\$ Hence the required quadratic equation is $\displaystyle \sf x^{2} - \frac{1}{12} x - \frac{1}{2} = 0$

Answer»

ong>GIVEN :-

TO FIND :-

SOLUTION :-

As we KNOW that the quadratic equation is given by,

$\\ : \implies \displaystyle \sf \:x^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0\\ \\$

Now, by SUBSTITUTING the values we get,

$\\ : \implies \displaystyle \sf \:x^{2} - \bigg( \frac{3}{4} - \frac{2}{3} \bigg)x + \bigg( \frac{3}{4} \times \frac{ - 2}{3} \bigg)= 0 \\ \\ \\$

$: \implies \displaystyle \sf \:x^{2} - \bigg( \frac{9 - 8}{12} \bigg)x + \bigg( \frac{ - 2}{4} \bigg) = 0 \\ \\ \\$

$: \implies \displaystyle \sf \:x^{2} - \frac{1}{12} x + \bigg( \frac{ - 1}{2} \bigg) = 0 \\ \\ \\$

$: \implies \underline{ \boxed{ \displaystyle \sf \bold{ \:x^{2} - \frac{1}{12} x - \frac{1}{2} = 0}}} \\ \\$

Hence the required quadratic equation is $\displaystyle \sf x^{2} - \frac{1}{12} x - \frac{1}{2} = 0$

Discussion