Advertisements
Advertisements
प्रश्न
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Advertisements
उत्तर
2x² – 3x + 1 = 0; x = -1.
Putting x = -1 in L.H.S. of equation
L.H.S. = 2(-1)2 - 3 x -1 + 1
= 2 + 3 + 1
= 6 ≠ 0 ≠ R.H.S.
Hence, x = -1 is not a root of the equation.
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 – 6x + 3 = 0
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
