Quadratic Equations Class 10 Mcq Test (100401)

If the roots of the equation (a²+b²)x²-2b(a+c)x+b²+c²=0 are equal, then: 

(a) 2b = a + c

(b) b² = ac

(c) \(b=\frac{2ac}{a+c}\)

(d) b = ac

Which of the following is a quadratic equation?  

(a) \(x^2+2x+1=(4-x)^2+3\)

(b) \(-2x^2=(5-x)(2x-\frac{2}{5})\)

(c) \((k+1)x^2+\frac{3}{2}x=7\), where k=−1

(d) \(x^3-x^2=(x-1)^3\)

If x = 1 is a common root of the equations ax² + ax + 3 = 0 and x² + x + b = 0, then ab is equal to:

(a) 3

(b) 3.5

(c) 6

(d) – 3 

The roots of the equation ax²+x+b=0 are equal, if:

(a) b²=4a

(b) b²<4a

(c) b²>4a

(d) ab=¼

If one root of the equation 2x²−10x+p=0 is 2, then the value of p is:

(a) −3

(b) −6

(c) 9

(d) 12

If the equation (a²+b²)x²−2(ac+bd)x+c²+d²=0 has equal roots, then:

(a) ad = cd

(b)  ad = bc

(c) \(ad=\sqrt{bc}\)

(d) \(ab=\sqrt{cd}\)  

For what value of k, x = 2 is a solution of kx² + 2x – 3 = 0?

(a) \(k=-\frac{1}{2}\)

(b) \(k=\frac{1}{2}\)

(c) \(k=-\frac{1}{4}\)

(d) \(k=\frac{1}{4}\)

Which of the following is a root of the equation 2x² – 5x – 3 = 0?  

(a) x = 3

(b) x = 4

(c) x = 1

(d) x = –3 

If the equation x² + 4x + k = 0 has real and distinct roots, then:

(a) k < 4

(b)  k > 4  

(c) k > 4 

(d)  k < 4

x=√2 is a solution of the equation:

(a) x²+√2 x−4=0

(b) x²−√2 x−4=0

(c) 3x² + 5x + 2 = 0    

(d) (a) and (b) both