Advertisements
Advertisements
प्रश्न
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Advertisements
उत्तर
6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
If x = `(-1)/(2)`, then
= `6(-1/2)^2 - (-1/2) - 2`
= `6 xx (1)/(4) + (1)/(2) - 2`
= `(3)/(2) + (1)/(2) - 2`
= `(4)/(2) - 2` = 0
∴ x = `(-1)/(2)` is its root
If x = `(2)/(3)`, then
= `6 xx (4)/(9) - (2)/(3) - 2`
= `(8)/(3) - (2)/(3) - 2`
= `(6)/(3) - 2` = 0
∴ x = `(2)/(3)` is also its root.
Hence `(-1)/(2), (2)/(3)` are both its root.
APPEARS IN
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
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).
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Equation (x + 1)2 – x2 = 0 has ____________ real root(s).
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
