Advertisements
Advertisements
Question
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Advertisements
Solution
x2 -5x+ 7= 0
b2 - 4ac
= (-5)2 - 4(1)(7)
= 25 - 28
= -3
Since discriminant is negative, hence the roots are imaginary.
APPEARS IN
RELATED QUESTIONS
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case.
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
