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CBSE - Class 10 Mathematics Quadratic Equations Worksheet

The graph of a quadratic equation is always a parabola.

a. True b. False

Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (ii) $kx (x – 2) + 6 = 0$

Solve the following quadratic equation for q: 9q²- 9(a+b)q + 2a²+ 5ab + 2b²= 0.

Determine the positive value of k for which the equation $x^{2} + kx + 64 = 0$ and $x^{2} - 8x + k = 0$ will both have real and equal roots

The roots of the equation $2x^{2}-6x+7=0$ are

real, unequal and rational

real, unequal and irrational

real and equal

imaginary

A polynomial with degree 2 is called quadratic equation.

a. True b. False

Find the value of k for which the equation $(3k + 1)x^{2} + 2(k + 1)x + 1$ has equal roots. Also find the roots.

solve for a : $\sqrt{3} a^{2} - 2\sqrt{2a} - 2\sqrt{3} = 0$

Find the roots of the quadratic equation $a^{2}b^{2}x^{2} + b^{2}x - a^{2}x - 1 = 0$

10.

Check whether the following are quadratic equations : (iii) $(x – 2)(x + 1) = (x – 1)(x + 3)$

11.

Find the roots of the following quadratic equations by factorisation: (i) $x^2 – 3x – 10 = 0$

12.

If the quadratic equation $(1 + a^{2})b^{2}x^{2} + 2abcx + (c^{2} - m^{2}) = 0$ , in x has equal roots, prove that $c^{2} = m^{2}(1 + a^{2})$

13.

The time taken by a person to cover 150 kms was $2\tfrac{1}{2}$ hours more than the time taken in the return journey. If he returned at a speed of 10km/hr more that the speed while going, find the speed per hour in each direction.

14.

Solve the following quadratic equation for p: $4 p^{2} + 4 bp - (a^{2} - b\sqrt{2}) = 0$

15.

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

16.

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.

17.

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

18.

If the roots of the quadratic equation $(b - c)x^{2} + (c - a)x + (a - b) = 0$ are equal prove that 2b = a + c

19.

130

150

120

20.

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

Worksheet Answers

Option A

q = 2a + b/3.

For equation I0 k = ± 16, ii) 16

Option D

Option A

k = 0, 1; x = -1/2

a = $\sqrt{6}$ , a = $-\sqrt{2/3}$

$x = -1/a^{2}$

12.

$c^{2} = m^{2}(1 + a^{2})$ , Proved

13.

Speed while going = 20 km/hr, while returning = 30 km/hr

14.

x = - (a + b)/2, x = a - b/2

15.

9, 10, 11.

16.

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

17.

k = 1, 3

18.

2b = a + c, proved

19.

Option B

20.

No it is not

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