Class 10 Maths Important Questions for Quadratic Equation
Given below are the Class 10 Maths Important Questions for Quadratic Equation
Concepts questions
Calculation problems
Multiple choice questions
Long answer questions
Fill in the blank's
Short Answer type
Question 1. State which all quadratic equations have real roots, no real roots
$x^2 + x+7=0$
$3x^2 +6x+1=0$
$9x^2 +x +3=0$
$11x^2 -12x-1=0$
$-13x^2 +3x+7=0$
$2x^2 -6x+3=0$
$x- \frac {1}{x}-3=0$, x≠0
$-x^2 -2x-2=0$
Solution Nature of roots of Quadratic equation
S.no
Condition
Nature of roots
1
$b^2 -4ac > 0$
Two distinct real roots
2
$b^2 -4ac = 0$
One real root
3
$b^2 -4ac < 0$
No real roots
Real roots: :(b), (d) ,(e),(f),(g)
No real roots : (a) ,(c),(h)
Question 2. Find the roots of the quadratic equation using factorization technique
a. $x^2-3x-10=0$
b. $x^2 -11x+30=0$ Solution
a.
$x^2-3x-10=0$
$x(x-5) +2(x-5)=0$
$(x+2)(x-5)=0$
So roots are x=-2 and 5
b. Roots are 5 and 6
Question 3. Find the roots of the quadratic equation using square method
a. $x^2 +4x-5=0$
b. $2x^2-7x+3=0$ Solution
a.
$(x+ \frac {4}{2})^2 -(\frac {4}{2})^2 -5=0$
$(x+2)^2-9=0$
$(x+2)^2=9$
$x+2=\pm 3$
x=1 or -5
b.
$(x-\frac {7}{4})^2 -(\frac {7}{4})^2 +3/2=0$
$(x-\frac {7}{4})^2= \frac {49}{16} - \frac {3}{2}=0$
$(x-\frac {7}{4})^2=\frac {25}{16}$
$x-\frac {7}{4}=\pm \frac {5}{4}$
or
x=1/2 or 3
Question 4. True or False statement
a. There are no reals roots of the quadratic equation $x^2+4x+5=0$
b. The roots of the equation $x^2-1=0$ are 1,-1
c. A quadratic equation can have at most 2 real roots
d. In a quadratic equation $ax^2 +bx+c=0$ ,if a and c are of same sign and b is zero ,the quadratic equation has real roots
e. In a quadratic equation $ax^2 +bx+c=0$ ,if a and c are of opposite sign, then quadratic equation will definitely have real roots
f. for k > 0,the quadratic equation $2x^2+6x-k=0$ will definitely have real roots
g. if the roots of the quadratic equation are rational, the coefficient of the term x will also be rational.
h. if the roots of the quadratic equation are irrational, the coefficient of the term x will also be irrational
i. Every quadratic equation will have rational roots
Solution
True
True
True
false
True
True
true
true
False
Multiple choice Questions
Question 7. Find a natural number whose square diminished by 84 is thrice the 8 more of given number
a. 21
b. 13
c.11
d. 12 Solution (d)
$x^2 -84=3(x+8)$
$x^2-3x-108=0$
x= 12 or -9
So answer is 12
Question 8. The roots of the quadratic equation
$x^2 +14x+40=0$ are
a.(4,10)
b.(-4,10)
c.(-4,-10)
d.(4,-10) Solution
$x^2 +14x+40=0$
$x^2 + 4x + 10x +40=$
$x(x+4) + 10(x+4)=0$
$(x+4)(x+10)=0$
x=-4 or -10
Answer (c)
Question 9. The equation
$x^5 +x+20=0$
a. is a quadratic equation
b. is not a quadratic equation Solution
It is not a quadratic equation Question 10. The roots of the quadratic equation
$x^2+2x+5=0$
a. are real
b. are not real Solution (b)
$b^2 - 4ac = 4 -20 =-16$
Answer is (b)
Question 11.
Which one of the following is not a quadratic equation?
a. $(x + 2)^2= 2(x + 3)$
b. $x^2 + 3x = (-1) (1 - 3x)^2$
c. $(x + 2) (x - 1) = x^2 - 2x - 5$
d. $x^3 - x^2 + 2x + 1 = (x + 1)^3$ Solution (b)
We can expand each of these expression and compare with $ax^2 + bx+x=0$.
Answer (c)
Question 12.
Find the roots of
$6x^2- \sqrt {2}x - 2 = 0$ by the factorisation of the corresponding quadratic polynomial.
a. $-\frac {\sqrt {2}}{3},\frac {\sqrt {2}}{2}$
b. $-\frac {\sqrt {1}}{3},\frac {\sqrt {2}}{2}$
c. $-\frac {\sqrt {2}}{3},\frac {\sqrt {2}}{5}$
d. None of the these Solution (b)
$6x^2- \sqrt {2}x - 2 = 0$
$6x^2 + 3 \sqrt {2}x -2\sqrt {2}x - 2 = 0$
$ 3x(2x - \sqrt {2}) - \sqrt {2}(2x - \sqrt {2})=0$
$(3x- \sqrt {2})(2x - \sqrt {2})=0$
or x = $-\frac {\sqrt {2}}{3},\frac {\sqrt {2}}{2}$
Answer (a)
Question 13.
Had Ram scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?
a. 15 marks
b. 10 marks
c. 12 marks
d. 20 marks Solution (b)
$9 (x +10) = x^2$
$x^2 - 9x - 90 = 0$
$(x + 6) (x -15) = 0$
Therefore, x = - 6 or x =15
Answer (a)
Match the Column
Question 14.
Match the roots with the quadratic equations
Solution
a -> iii, vi
b-> iii, vii
c -> iii, v
d -> iv, viii
e. i, ii