Advertisements
Advertisements
प्रश्न
Which of the following equations has the sum of its roots as 3?
विकल्प
2x2 – 3x + 6 = 0
–x2 + 3x – 3 = 0
`sqrt(2)x^2 - 3/sqrt(2)x + 1` = 0
3x2 – 3x + 3 = 0
उत्तर
–x2 + 3x – 3 = 0
Explanation:
The sum of the roots of a quadratic equation ax2 + bx + c = 0, a ≠ 0 is given by,
Coefficient of x / coefficient of x2 = `-(b/a)`
(A) Given, 2x2 – 3x + 6 = 0
Sum of the roots = `(-b)/a`
= `(-(-3))/2`
= `3/2`
(B) Given, –x2 + 3x – 3 = 0
Sum of the roots = `(-b)/a`
= `(-(3))/(-1)`
= 3
(C) Given, `sqrt(2)x^2 - 3/sqrt(2)x + 1` = 0
`2x^2 - 3x + sqrt(2)` = 0
Sum of the roots = `(-b)/a`
= `(-(-3))/2`
= `3/2`
(D) Given, 3x2 – 3x + 3 = 0
Sum of the roots = `(-b)/a`
= `(-(-3))/3`
= 1
APPEARS IN
संबंधित प्रश्न
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
