Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x(1 – x) – 2 = 0
Advertisements
उत्तर
The equation x(1 – x) – 2 = 0 has no real roots.
Simplifying the above equation,
x2 – x + 2 = 0
D = b2 – 4ac
= (–1)2 – 4(1)(2)
= 1 – 8 < 0
Hence, the roots are imaginary.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Solve x2/3 + x1/3 - 2 = 0.
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Which of the following equations has no real roots?
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
Which of the following equations has the sum of its roots as 3?
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
