Roots of a Quadratic Equation
Trending Questions
Q.
If x2+y2=25, xy=12, then complete set of x=
{3, 4}
{−3, −3}
{3, 4, −3, −4}
{3, −3}
Q. If the product of the roots of the quadratic equation mx2−2x+(2m−1)=0 is 3, then the value of m is
- 1
- 2
- −1
- 3
Q. If a, b, c are three distinct positive real numbers, then the number of real root(s) of ax2+2b|x|+c=0 is
- 0
- 2
- 4
- 1
Q. How many roots the equation x−2x−1=1−2x−1 have
- One
- Two
- Infinite
- None
Q.
If , then is equal to:
Q. The value of P for which the equation (P3−3P2+2P)x2+(P3−P)x+P3+3P2+2P=0 has exactly one root at infinity is
- 1
- −1
- 0
- 2
Q. The number of real solutions of 1+|ex−1|=ex(ex−2) is
- 0
- 1
- 2
- 4
Q.
Using quadratic formula solve for :
Q. Given that the real numbers s, t satisfy 19s2+99s+1=0, t2+99t+19=0 and st≠1, then the absolute value of st+4s+1t is
- a prime number
- divisible by 19
- divisible by 5
- divisible by 2
Q. The value of P for which the equation (P3−3P2+2P)x2+(P3−P)x+P3+3P2+2P=0 has exactly one root at infinity is
- 1
- −1
- 0
- 2
Q. A two-digit positive number is such that the product its digits is 8. If 18 is added to the number then the digits are reversed, then the original number is
Q. Let α, β be the roots of x2−x−1=0 (α>β) and m, n∈Z, k∈W such that ak=mαk+nβk. If a4=35, then the value of 3m+2n is equal to
- 40
- 85
- 25
- 75
Q. The difference between a natural number and twice its reciprocal is 477, then the number is
- 2
- 4
- 8
- 7
Q. If the roots of the equation 4x2+ax+3=0 are in ratio of 1:2, then value(s) of a is/are
- 3√6
- −3√6
- −√6
- √6
Q.
The roots of the equation ix2−4x−4i = 0 are
2 , -2i
-2i, -2i
2i
2i, 2i
Q. The root(s) of the equation (log3x)2−log3x=6 is/are
- 19
- √3
- 9
- 27
Q. If a, b, c are distinct rational numbers, then the roots of the quadratic equation (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0 are
- rational and distinct
- rational and equal
- irrational
- imaginary
Q. If the equation (3−log12√4(x−2))2−4∣∣3−log12√4(x−2)∣∣+3=0 has integral roots α and β such that |α|+|β−1|=|α−1|+|β|, then |α+β| is equal to
Q. The number of values of x satisfying the equation (x2+7x+11)(x2−4x−21)=1 is
- 6
- 4
- 2
- 5
Q. The roots of the equation 3x−5+2xx−3=5 are (where x≠3, 5)
- 5
- 7
- 6
- 4
Q. If 2x2+x−1=0, then the value of the expression 2x−1x+(4x2+1x2)2+(8x3−1x3)3 is
Q. The roots of the equation x2+|x|−2=0 is/are
- −1
- −2
- 1
- 2
Q. The quadratic equation whose roots are −4 and 6 is given by
- x2+2x−24=0
- x2−2x−24=0
- x2−2x+24=0
- x2−4x−24=0
Q. The difference between a natural number and twice its reciprocal is 477, then the number is
- 2
- 4
- 8
- 7
Q. The sum of the roots of equation log2(32+x−6x)=3+xlog2(32) is
- 3
- 7
- 9
- 5
Q. Let α and β be the roots of x2−6x−2=0, with α>β . If an=αn−βnforn≥1, then the value of a10−2a82a9is
- 2
- 3
- 4
- 1
Q. Let A={x∈R:x2−|x|−2=0} and B={α+β, αβ} where α, β are real roots of the quadratic equation x2+|x|−2=0. If (a, b)∈A×B, then the quadratic equation whose roots are a, b is
- x2−2x=0
- x2−x−2=0
- x2+2x=0
- x2+3x+2=0
Q. The value of
x=1+13+12+13+12+.....∞ is
x=1+13+12+13+12+.....∞ is
- √53
- √32
- −√32
- −√53
Q. Suppose a2=5a−8 and b2=5b−8. Then the equation whose roots are ab and ba is
- 6x2−5x+6=0
- 9x2−8x+9=0
- 8x2−9x+8=0
- 8x2+9x+8=0
Q. The number of real solutions of the equation |x|2−3|x|+2=0 are
- 1
- 3
- 4
- 2