Quadratic Equations Class 10 Mcq Test (100401)

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

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 x = 2 is a root of the equation 3x² – 2kx + 5 = 0, then k is equal to:

(a) \(\frac{4}{17}\)

(b) \(\frac{17}{4}\)

(c) \(\frac{1}{17}\)

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

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

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

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 

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) \(ab=\sqrt{cd}\)  

If ax² + bx + c = 0 has equal roots, then c is equal to:

(a) \(-\frac{b}{2a}\)

(b) \(\frac{b}{2a}\)

(c) \(-\frac{b^2}{4a}\)

(d) \(\frac{b^2}{4a}\)

If ½ is a root of the equation \(x^2+kx-\frac{5}{4}=0\), then the value of k is: 

(a) 2

(b)  – 2

(c) \(\frac{1}{4}\)

(d) \(\frac{1}{2}\)