Question

By using the quadratic formula solve quadratic equation y² + 1/2 y -1 =0​

Answer 1

Answer:-

$\sf{\frac{-1+\sqrt17}{4} \ and \ \frac{-1-\sqrt17}{4} \ are \ the \ roots.}$

Given:

• The given quadratic equation is $\sf{y^{2}+\frac{1y}{2}-1=0}$

To find:

• Roots of the equation.

Solution:

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{y^{2}+\frac{1y}{2}-1=0}$

$\sf{Here, \ a=1, \ b=\frac{1}{2} \ and \ c=-1}$

$\sf{b^{2}-4ac=(\frac{1}{2})^{2}-4(1)(-1)}$

$\sf{\therefore{b^{2}-4ac=\frac{1}{4}+4}}$

$\sf{\therefore{b^{2}-4ac=\frac{1+16}{4}}}$

$\sf{\therefore{b^{2}-4ac=\frac{17}{4}}}$

$\sf{By \ formula \ method}$

$\sf{y=\frac{-b+\sqrt{b^{2}-4ac}}{2} \ or \ \frac{-b-\sqrt{b^{2}-4ac}}{2}}$

$\sf{\therefore{y=\frac{\frac{-1}{2}+\frac{\sqrt17}{2}}{2} \ or \ \frac{\frac{-1}{2}-\frac{\sqrt17}{2}}{2}}}$

$\sf{\therefore{y=\frac{-1+\sqrt17}{4} \ or \ \frac{-1-\sqrt17}{4}}}$

$\sf\purple{\tt{\therefore{\frac{-1+\sqrt17}{4} \ and \ \frac{-1-\sqrt17}{4} \ are \ the \ roots.}}}$