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Ivahew [28]
3 years ago
11

Find a formula for the sum S of the solutions of the quadratic equation ax²+bx+c=0 .

Mathematics
1 answer:
Deffense [45]3 years ago
8 0

Answer:

S = -\frac{b}{a}

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = (x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this problem, the sum S of the solutions of a quadratic equation is:

S = x_{1} + x_{2}

So

S = \frac{-b + \sqrt{\bigtriangleup}}{2*a} + \frac{-b - \sqrt{\bigtriangleup}}{2*a}

They have the same denominators, so we can keep the denominators and sum the numerators.

S = \frac{-b + \sqrt{\bigtriangleup} - b - \sqrt{\bigtriangleup}}{2a}

S = \frac{-2b}{2a}

S = -\frac{b}{a}

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Activity: A flagpole has cracked 1.7 m from the ground and fallen over, as if hinged. The top of the flagpole hit the ground 3 m
Anastasy [175]

Answer:

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Step-by-step explanation:

Given:

Height of remain pole (p) = 1.7 m

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Height of flagpole before it fell

Computation:

Using Pythagorean theorem

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Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.
lilavasa [31]

Answer:

<em>First even integer: 6</em>

Step-by-step explanation:

<u>Inequalities</u>

Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.

The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:

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