Advertisements
Advertisements
प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Advertisements
उत्तर
The given quadratic equation is
x2 + 2x + 4 = 0
Here, a = 1, b = 2 and c = 4
Descriminant
= b2 - 4ac
= (2)2 - 4 x 1 x 4
= 4 - 16
= -12 < 0
Hence, the given equation has no real roots.
संबंधित प्रश्न
Find that value of p for which the quadratic equation (p + 1)x2 − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Form the quadratic equation if its roots are –3 and 4.
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
If a = 1, b = 4, c = –5, then find the value of b2 – 4ac.
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
