## CBSE CLASS 10 QUADRATIC EQUATIONS - RIVISION NOTES AND PRACTICE QUESTIONS

**CBSE Class 10 Sample Papers of All Subjects with Solutions**

### QUADRATIC EQUATIONS WORKSHEET FOR CLASS 10

**1.**Determine whether 3 is a root of the equation$$\sqrt{{x}^{2}-4x+3}+\sqrt{{x}^{2}-9}=\sqrt{4{x}^{2}-14x+6}$$

**2.**If one root of $a{x}^{2}+bx+c=0$is double the other ,then prove $2{b}^{2}=9c$

**3.**Solve the equation$\frac{4}{x}-3=\frac{5}{2x+3};x\ne 0,-\frac{3}{2},forx$

**4.**Solve for x :$\frac{x-4}{x-5}+\frac{x-6}{x-7}=\frac{10}{3};x\ne 5,7$

**5.**The difference of two natural number is 5 and the difference of their reciprocal is 1/10, Find the numbers.

**(CBSE DELHI 2014)**

**6.**Two pipes running together can fill a cistern in 40/13 minutes. If one pipe takes 3 minutes more then the other to fill it, find the time in which each pipe would fill the cistern.

**(HOTS)**

**7.**A man has Rs. 10,000 with him. He calculated that he could spend Rs x everyday on his transportation. He spent Rs (x - 50) everyday and use the remaining amount for more 10 days.

**8.**Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of other two by 60. Find the numbers.

**(CBSE 2016)**

**9.**Find the value of k for the quadratic equation kx ( x - 2 ) + 6 = 0 , so that it has two equal roots.

**10.**If the roots the equation $({a}^{2}+{b}^{2}){x}^{2}-2b\left(a+c\right)x+\left({b}^{2}+{c}^{2}\right)=0$ are equal, then find the value of b

^{2}

**11.**If -5 is a root of the quadratic equation $2{x}^{2}+px-15=\mathrm{0\; and\; the}$quadratic equation $p\left({x}^{2}+x\right)+k=0$ has equal roots, then find the value of k.

**12.**A train takes two hours less for a journey of 300 km. If its speed is increased by 5 km per hours from its usual speed, Find the usual speed of train.

**13.**A rectangular field is 20 m long and 14 m wide their is a path of equal width all around it, having an area of 111 sqm find the width of the path.

**( CBSE 2013,2012)**

**14.**At t min past 2 pm the time needed by the minute hand of a clock to show 3 pm was found to be 3 minutes less then t

^{2}/4 minutes. Find t.

**15.**A factory kept increasing its output the same percentage every year Find the percentage, If it is known that it's output is doubled in the last two years.

**( CBSE 2013,2015)**

**Read More : Class 10 Probability Important Questions with Answers**

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