Advertisements
Advertisements
Question
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Advertisements
Solution
3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
x = 5,
3(5)2 - 13 x 5 - 10
= 75 - 65 - 10
= 75 - 75
= 0
∴ x = 5 is its root
if x = `(-2)/(3)`, then
`3(-2/3)^2 - 13 xx (-2)/(3) - 10`
= `(3 xx 4)/(9) + (26)/(3) - 10`
= `(4)/(3) + (26)/(3) - 10`
= `(30)/(3) - 10`
= 10 - 10
= 0
∴ x = `(-2)/(3)` is also its root.
Hence both 5, `(-2)/(3)` are its roots.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
