Given below are the class 10 quadratic equations extra questions
Short Answer questions
True and false
Multiple choice questions
Match the column
Long answer type
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)
True and False
Question 2. 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 3. 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 4. 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 5. 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 6. 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 7.
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 8.
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 9.
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 10.
Match the roots with the quadratic equations Solution
a -> iii, vi
b-> iii, vii
c -> iii, v
d -> iv, viii
e. i, ii
Long Answer type
Question 11. 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 12. 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
Summary
This Class 10 Maths Extra Questions for Quadratic Equation along with solutions is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.
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