NCERT Solutions for Chapter: Quadratic Equations, Exercise 1: Exercise

Find all possible value(s) of $x$ for the following equation to be true.

$\sqrt{\left(15-2x\right)}-x=0$

Show your steps and give valid reasons.

The roots of the equation below are real numbers.

$2x^2-20x+c=0$

For what value of $c,$ the roots will be equal$?$ Show your steps and give valid reasons.

When a marble is dropped from an initial height, $d$ metres, with an initial speed, $v$ m/s, the height of the marble at time $t$ is represented by $h\left(t\right)=vt-2t^2+d.$

A marble is dropped from a height of $48$ m with an initial speed, $10$ m/s. How long does it take for the marble to hit the ground$?$ Show your steps and give valid reasons.

Find the solution(s) of the following equation.

$\left(y-1\right)\left(y-3\right)\left(\frac{1}{y-3}+\frac{2y}{y-1}\right)=2, y\ne 1,3$

Show your steps and give valid reasons.

The graph below represents the path of a ball thrown by Ankush. The maximum height, $h,$ the ball reaches with respect to time, $t,$ is represented by the polynomial $h\left(t\right)=-t^2+\frac{19}{4}t+\frac{5}{4}.$

How long will it take for the ball to reach the ground$?$ Show your steps.

Shown below is the graph of a quadratic polynomial, $y\left(x\right)=p{x}^2+qx+r.$

Find the nature of the roots of the quadratic equation, $p{x}^2+qx+r=0.$ Give a reason for your answer.

Which of the following is not a method of solving a quadratic equation?

The size of a screen is an important factor in designing a web page. The page can be opened on different screen sizes but during the initial designing stage, one screen area is considered as the safe area. The content in the safe area can be viewed without horizontal and vertical scrolling of the web page. The safe area of a web page is $40$pixels less than the width and $190$pixels less than the height of the display screen.

Which of the following expression represents the safe area for the screen whose screen height is $200$pixels less than the screen width ($w$)?