# BHARDWAJ CLASSES

## 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$x 2 −4x+3 + x 2 −9 = 4 x 2 −14x+6$

2. If one root of is double the other ,then prove $2{b}^{2}=9c$

3. Solve the equation

4. Solve for x :
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 $\left({a}^{2}+{b}^{2}\right){x}^{2}-2b\left(a+c\right)x+\left({b}^{2}+{c}^{2}\right)=0$ are equal, then find the value of b2
11. If  -5 is a root of the quadratic equation 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 t2/4 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)

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