Theory of Equations

If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then
1. p = 0
2. p = -2
3. p = ±2
4. p =2
The sum of the roots of the quadratic equation 3x² – 9x + 5 = 0 is
1. -3
2. 6
3. 3
4. 2
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
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and find the roots 8 and 2. Sohan commits a mistake in the coecient of x. The correct roots are
1. 9,1
2. -9,1
3. 9,-1
4. -9,-1
The roots of the quadratic equation 6x² – x – 2 = 0 are
1. 2/3,1/2
2. -2/3,1/2
3. 2/3,-1/2
4. -2/3,-1/2
The polynomial equation x (x + 1) + 8 = (x + 2) {x – 2) is
1. linear equation
2. quadratic equation
3. Cubic equation
4. None
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
The quadratic equation whose one rational root is 3 + √2 is
1. x² – 7x + 5 = 0
2. x² + 7x + 6 = 0
3. x² – 7x + 6 = 0
4. x² – 6x + 7 = 0
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,∞]
The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is
1. ±√6
2. ±4
3. ±3√2
4. ±2√6
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 one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, the value of q is
1. 49/4
2. 4/49
3. 4
4. 49
If a, p are the roots of the equation (x – a) (x – b) + c = 0, then the roots of the equation (x – a) (x – P) =c are
1. a, b
2. a, c
3. b, c
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
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

Theory of Equations

Quiz