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CBSE Questions for Class 10 Maths Quadratic Equations Quiz 10 - MCQExams.com

Which one of the following is the quadratic equation?
  • 5x3=x2
  • x(x+5)=4
  • n1=2n
  • 1x2(x+2)=x
The integral values of m for which the roots of the equation mx2+(2m1)x+(m2)=0 are rational are given by the expression [where n is integer ] 
  • n2
  • n(n+2)
  • n(n+1)
  • none of these
Which among the below are quadratic equations?

  • 5x3=x2
  • x(x+5)=2
  • n1=2n
  • 1x2(x+2)=2
If ax2+bx+c=0 then quadratic formula is
  • x=b±b24ac2a
  • x=b±b2+4ac2a
  • x=b+b24ac2a
  • x=bb24ac2a
Discriminant of quadratic equation 33x2+10x+3=0
  • 10
  • 64
  • 46
  • 30
Let a,b,c be the lengths of sides of a scalene triangle. If the roots of the equation x2+2(a+b+c)x+3λ(ab+bc+ca)=0 (λR) are real then
  • λ<43
  • λ>53
  • λ(13,53)
  • λ(43,53)
The equation 2x2x25=x22x3, where x is real has 
  • No real solution
  • Exactly one real solution
  • Exactly two real solutions
  • Exactly four real solutions
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
  • Assertion is correct but Reason is incorrect.
  • Assertion is incorrect but Reason is correct.
All solutions of the equation 4x240x+51=0 lie in the interval 
  • (2310,8310)
  • (2310,152)
  • (7,8310)
  • none of these
The values of a for which both the roots of the equation (a6)x2=a(x3)  are positive and are given by
  • (0,6)
  • (0,7211)
  • (6,7211)
  • (7213,6)
The roots of (xa)(xc)+k(xb)(xd)=0 are real and distinct for all real k if 
  • a<b<c<d
  • a>b<c<d
  • a<b>c<d
  • a<b=c<d
The quadratic equation x22xλ=0,λ0,
  • cannot have a real root if λ<1
  • can have a rational root if λ is a perfect square
  • cannot have an integral root if n21<λ<n2+2n where n=0,1,2,3,.....
  • none of these
If 1 is a root of the equations ay2 + ay+3=0 and y2+ y+b=0, then find the value of ab
  • 3
  • 4
  • 5
  • 6
If x2(a+b+c)x+(ab+bc+ca)=0 has non real roots, where a,b,cR+, then a,b,c
  • Can be the sides of a triangle
  • Cannot be the sides of triangle
  • Nothing can be said
  • None of these
The value of x26x+13 can never be less than
  • 4
  • 5
  • 4.5
  • 7
The number of values of k for which (x2(k2)x+k2)(x2+kx+(2k1)) is a perfect square
  • 1
  • 2
  • 3
  • 0
Find the root(s) of the equation y+y+5=7
  • 11
  • 4
  • 4 and 11
  • ±4
  • none of these
If α,β are the roots of ax2+2bx+c=0 and that of Ax2+2Bx+C=0 be α+δ,β+δ then the value of b2acB2AC is
  • (aA)2
  • (Aa)2
  • 0
  • 1
The roots of the equation (xa)(xb)+(xb)(xc)+(xc)(xa)=0 are
  • positive
  • negative
  • real
  • imaginary
If the quadratic equation x2mx4x+1=0 has real and distinct roots, then the values of m are
A.  (,6)
B.  (,3)   
C.  (2,)  
D.  (2,)
  • A or C
  • A or D
  • B or C
  • B or D
Let f(x)=x23x+4, then the value of x which satisfies f(1)+f(x)=f(1)f(x) is
  • 1
  • 2
  • 1 or 2
  • 1 and 0
The equation 9y2(m+3)+6(m3)y+(m+3)=0, where m is real has real roots then 
  • m<0
  • m>0
  • m0
  • m0
If x2+(ab)x+(1ab)=0, where a,bR, the value of a such that the equation has distinct real roots for all value of b are
  • a>1
  • a<1
  • a>2
  • a<2
A ray emanating from (6,2) is incident on ellipse (x1)245+(y2)220=1 at (4.6) The equation of reflected ray (after 1st reflection ) is  
  • x - 2y + 8 =0
  • x + 2y + 8 =0
  • x + 2y - 8 = 0
  • x - 2y - 8 =0
 The number of real roots of the equation (x1)2+(x2)2+(x3)2=0 is :
  • 1
  • 2
  • 3
  • None of these
Given that r and s are constants , the solution of the quadratic equation, rx2=1sx+3 , is:

  • x=12sr±1s2+12r2r
  • x=12sr±1s212r2sr
  • x=s2r±1s212r2r
  • x=s2r±s212sr2sr
If the expression x2+2(a+b+c)x+3(bc+ca+ab) is a perfect square, then
  • a=b=c
  • a=±b=±c
  • a=bc
  • None of the above
Number of possible value(s) of integer 'a' for which the quadratic equation x2+ax+16=0 has equal roots, is
  • 4
  • 6
  • 2
  • none of these
If, for a positive integer n, the quadratic equation, x(x+1)+(x+1)(x+2)++(x+1n1)(x+n)=10n has two consecutive integral solutions, then n is equal to
  • 11
  • 12
  • 9
  • 10
If the root of the equation x2+px+q=0 differ from the roots of the equation x2+qx+p=0 by the same quantity then 
  • p+q+1=0
  • p+q+2=0
  • p+q+4=0
  • None of these
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