If The Sum Of Roots Of A Quadratic Equation Is -2 And The Product Is 3, Find The Equation?

If the sum of roots of a quadratic equation is -2 and the product is 3, find the equation?

x² + 2x + 3 = 0
x² - 2x + 3 = 0
x² + 2x - 3 = 0
None of these

Explanation

For quadratic ax² + bx + c = 0:

Sum of roots = -b/a

Product of roots = c/a

Take a = 1, then:

-b = sum = -2 → b = 2

c = product = 3

So equation: x² + 2x + 3 = 0

Last verified on 23-06-2026

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If the point is (a,−a), then it lies on which line?

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Find the sum: 2×1^2 +4×2^2 +6×3^ +⋯+20×10^2

76,440
77,000
77,440
6050

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Explanation

Given:

2 \times 1^^{2} + 4 \times 2^^{2} + 6 \times 3^^{2} + \dots + 20 \times 1 0^2

Write the terms as:

2 (1^^{3}) + 2 (2^^{3}) + 2 (3^^{3}) + \dots + 2 (1 0^^{3})

= 2 (1^^{3} + 2^^{3} + 3^^{3} + \dots + 1 0^^{3})

Using the formula:

1^3+2^3+cdots+n^3=left[frac{n(n+1)}{2}right]^2

For $n = 10$ :

= 2 [10 ( 11 )/2]^^{2}

= 2 (55)^^{2}

= 2 \times 3025

6050

$Last updated 27-07-2026 by NA$

If x+y=16 and x−y=3, then x^2 −^ 2 =?

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Explanation

Given:

$x + y = 16$
$x-y=3$

Using the identity:

$x^{2} - y^{2} = (x + y) (x - y)$ $= 16 \times 3$

$= 48$

$Last updated 27-07-2026 by NA$

If y is directly proportional to x and x = 2, y = 5, then find y when x = 7?

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The volume of a cube is 275. The length of one side of the cube is?

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