QUADRATIC EQUATIONS

Identify the quadratic equation from the following.
1. m+1/m=1,m≠0
2. m²+1/m=1,m≠0
3. x²−1/x=1,x≠0
4. x²+2√x−1=0
Which of the following statements is correct?
1. x=2is a root of 2x²+5x+1=0
2. x=3 is not a root of x²+3x−5=0
3. x=−1 is not a root of 5x²−x−1=0
4. All
Find the value of ?a? for which m=1/√3 is a root of the equation.am²+(√3−√2)m−1=0.
1. √2
2. 2
3. √6
4. 5
Which of the following equations has no real roots?
1. x²−4x+3√2=0
2. x²+2x-6√2=0
3. x²-4x-3√2=0
4. None
The sides of two square plots are (2x −1)mand(5x+4)m. The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.
1. 50m
2. 20m
3. 26m
4. 39m
Which of the following are the roots of the equation|x|²+|x|−12=0?
1. 3,3
2. 3,-3
3. 1,-1
4. All
The age of a man is the square of his son's age. One year ago, the man's age was eight times the age of his son. What is the present age of the man?
1. 60 years
2. 49 years
3. 30 years
4. 40 years
If the roots of the equation 3ax²+2bx+c=0 are in the ratio 2 : 5, then
1. 8ac=25b²
2. 6ac=19b²
3. 40b²=75ac
4. 8b²=25ac
The sum of squares of two consecutive positive even integers is 340. Find them.
1. 12, 14
2. 4, 6
3. 6, 8
4. 10, 12
Find the relationship between the coefficients of the equation rx²+sx+1=0, such that α:β=3:4 where α,βare roots of equation.
1. 12s²=49rt
2. 22s²=-49rt
3. 59s²=12rt
4. 59t²=49r5
Which of the following are the roots of|y|²−|y|−20=0?
1. 4
2. 5
3. 6
4. ±5
The equation 9y²(m+3)+6(m−3)y+(m+3)=0, where m is real, has real roots. Which of the following is true?
1. m=0
2. m<0
3. m≤0
4. m≥0
Find the maximum or minimum value of the quadratic expression,x²−5x+8, which ever exists.
1. y=1/2
2. y=7/4
3. y=0
4. No solution
Which of the following quadratic equations have equal roots?
1. 2x²−3x+5=0
2. 3x²−4√3x+4=0
3. 2x²−6x+3=0
4. x+1/x=1
If α and β are the root of the equation2x²−3x−7=0 then the value ofαβ²+α²β+αβ are.
1. 6
2. -35/4
3. 3/4
4. -15/8
If the sum of the roots of ax²+2bx+3c=0 is equal to the sum of the squares of their reciprocals, then 9bc²+2ab²
1. 18abc
2. 3a²c
3. ab+bc+2ca
4. 18a²c+7b²
If the roots of the quadratic equationx²−kx+k²−3=0 are real, then the range of the values of k is
1. [−2,2]
2. [−∞,−2]∪[2,∞]
3. [−3,3]
4. [−∞,−3]∪[3,∞]
When is a real number 'a' called the zero of the polynomial f(x)?
1. f(0)=a
2. f(a)=f(0)
3. f(a)=0
4. f(±a)=±a
If the roots of the quadratic equation ax²+bx+c=0are α and β, then the equation whose roots are α² and β² is
1. a²x²−(b²−2ac)x+c²=0
2. (a²−r)x²+(b²−r)x+c²r=0
3. (a²−ac)x²+(b²+2ac)x+cv=0
4. 2a²x²−(b²+2ac)x+2c²=0
If a and b can take value 1, 2, 5, 6, then the number of the equations of the form ax²+bx+1=0 having real roots is
1. 11
2. 9
3. 15
4. none
If sinθ, cosθ are roots of the equationax²−2bx+3c=0, then
1. 4b²−a²−6ac=0
2. a²+b²+c²+abc=0
3. a²+b²+2abc−c²=0
4. a²+b²−2ac=0
tan A, tan B are roots of3x²−5x+6=0. then sin2(A+B)
1. 14/15
2. 25/34
3. 13/25
4. 11/46
A quadratic equation ax²+ bx + c = 0 has , if b²– 4ac > 0,
1. two distinct real roots
2. two equal roots
3. no real roots
4. None
A quadratic equation ax²+ bx + c = 0 has , if b²– 4ac = 0,
1. two distinct real roots
2. two equal roots
3. no real roots
4. None
A quadratic equation ax²+ bx + c = 0 has , if b²– 4ac < 0,
1. two distinct real roots
2. two equal roots
3. no real roots
4. None

QUADRATIC EQUATIONS

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