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CBSE - Class 10 Mathematics Quadratic Equations Worksheet

Find the roots of the following quadratic equations by factorisation: (iv) $2x^2 – x + \frac{1}{8} = 0$

Solve for p: $\sqrt{6p} + 7 - (2p - 7) = 0$

Find the value of k for which the quadratic equation $(k - 2)x^{2} + 2(2k - 3) + (5k - 6) = 0$ has equal roots

Check whether the equation a(a+1) + 8 = (a+2)(a-2) is a quadratic equation.

Find the roots of the following quadrtic equation: $15 q^{2} - 10\sqrt{6}q + 10 = 0$

A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

The sum of squares of two consecutive odd number is 394. Find the numbers.

the two parts into which 57 should be divided so that their product is 782, are

43 and 14

33 and 24

34 and 23

44 and 13

A two digit number is four times the sum of the dgits. It is also equal to 3 times the product of digits. Find the number?

10.

Solve the quadratic equation:

3/2

11.

Find the roots of the following quadratic equations by factorisation: (v) $100x^2 – 20x + 1 = 0$

12.

Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (i) $2x^2 + kx + 3 = 0$

13.

Is it possible to design a rectangular park of perimeter $80$ m and area $400$ $m^2$? If so, find its length and breadth.

14.

Two water taps running together can fill a tank in 9 hours 36 mins. The tap of larger diameter takes 8 hours less that the smaller one to fill the tank separately. Find the time in which each tap would fill the tank separately.

15.

Find a natural number whose square diminished by 84 is thrice of 8 more of given number

16.

Find the non zero value of K, for which the quadratic equation $kx^{2} + 1 - 2(k - 1)x + x^{2} = 0$ has equal roots hence find root of the equation

17.

In a class test, the sum of the marks obtained by a student in English and Hindi is 28. Had he got 3 more marks in English and 4 less marks in Hindi, the product of the marks would have been 180. Find the marks in two subjects.

18.

Represent the following situations in the form of quadratic equations : (iii) Rohan’s mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan’s present age.

19.

A natural number when increased by 12, equals 160 times its reciprocal. Find the number

20.

Solve for p: 10p - 1/p = 3 , $\neq 0$

Worksheet Answers

p= 7 or p = 3/2

k = 1, 3

No it is not

$q = \sqrt{2}/\sqrt{3}, \sqrt{2}/\sqrt{3}$

6 km/hr

13, 15

Option C

10.

Option A

14.

16 hrs and 24 hrs

15.

Option B

16.

k = 0, 3

17.

Case 1, English =9, Hindi =19, case 2, English =12, Hindi = 16

19.

Option B

20.

x = 1/2, -1/5

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