Neha Tyagi and Amit Rastogi Solutions for Chapter: Quadratic Equations, Exercise 4: Exercise

Find whether the following equations have real roots. If real root exist, Find them

$8x^2+2x-3=0$

If $a \mathrm{and} b$ are the roots then, find $16k$ if $a^2+b^2=k$.

Find whether the given equation have real roots. If real root exist, Find them

$-2x^2+3x+2=0$

If $a \mathrm{and} b$ are the roots of the equation then find $4k$ if $a^2+b^2=k$

Find whether the following equations have real roots. If real root exist, Find them
$5x^2-2x-10=0$

If one of the root is $\frac{1-\sqrt{k}}{5}$, find $k$

Find whether the following equations have real roots. If real root exist, Find them.

$\frac{1}{2x-3}+\frac{1}{x-5}=1, x\ne \frac{3}{2}, 5$

If one of the root is $4+6\sqrt{k}$, then find $k$?

Find whether the following equations have real roots. If real root exist, Find them

$x^2+5\sqrt{5}x-70=0$

If one of the root is $2\sqrt{k}$, find $k$

At present Asha's age ( in years) is $2$ more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age. Asha's age would be one year less than $10 \mathrm{times}$ the present age of Nisha. Find the Present ages of both Asha and Nisha.

In the centre of a rectangular lawn of dimensions $50 \mathrm{m}\times 40 \mathrm{m}$, a rectangular pond has to be constructed, so that the area of the grass surrounding the pond would be $1184 {\mathrm{m}}^2$ [see figure]. Find the length and breadth of the pond.

At $\mathrm{t} \min$past$2 \mathrm{pm}$, the time needed by the minute hand of a clock to. Show $3 \mathrm{pm}$ was found to be $3 \min$less than $\frac{t^2}{4}$ min. Find $t$.