Advertisements
Advertisements
प्रश्न
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Advertisements
उत्तर
x2 +3x+1=0
b2 - 4ac
= (3)2 - 4(1)(1)
= 9 - 4
= 5
Since discriminant is positive, hence the roots are real and irrational.
APPEARS IN
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
If the roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then prove that 2b = a + c.
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
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.
