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MAXImum [283]
2 years ago
7

Solve y = ax² + c for x.

Mathematics
1 answer:
Furkat [3]2 years ago
3 0

In the quadratic equation y = ax^{2} + c ,the value of x = ± \sqrt \frac{y-c}{a}

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming a\neq o

First, subtract c from both the sides to get:

y-c=ax^{2}

then, divide both sides by a and transpose to get:

x^{2} =\frac{y-c}{a}

So, x must be a square root of \frac{y-c}{a}  and we can deduce:

x= ± \sqrt \frac{y-c}{a}

Learn more about quadratic equations here brainly.com/question/1214333

#SPJ9

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Which expression can be used to check the answer to 56+(-14)=n?
Delvig [45]

Answer: n = 42

Step-by-step explanation:

56 - 14 = 42

If + and - are right next to each other, the + cancels out.

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Please answer this question​
Tems11 [23]

\bold{\huge{\underline{ Solution }}}

<h3><u>Given </u><u>:</u><u>-</u><u> </u></h3>

• \sf{ Polynomial :- ax^{2} + bx + c }

• The zeroes of the given polynomial are α and β .

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u><u> </u></h3>

Here, we have polynomial

\sf{ = ax^{2} + bx + c }

<u>We </u><u>know </u><u>that</u><u>, </u>

Sum of the zeroes of the quadratic polynomial

\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}

<u>And </u>

Product of zeroes

\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}

<u>Now, we have to find the polynomials having zeroes </u><u>:</u><u>-</u>

\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}

<u>T</u><u>h</u><u>erefore </u><u>,</u>

Sum of the zeroes

\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}

\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}

\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}

\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}

\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}

\bold{{\dfrac{ -bc - ab}{ac}}}

Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac

<h3><u>Now</u><u>, </u></h3>

Product of zeroes

\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}

\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}

\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}

\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}

Hence, The product of the zeroes are c/a + a/c + 2 .

<u>We </u><u>know </u><u>that</u><u>, </u>

<u>For </u><u>any </u><u>quadratic </u><u>equation</u>

\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }

\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}

Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .

<h3><u>Some </u><u>basic </u><u>information </u><u>:</u><u>-</u></h3>

• Polynomial is algebraic expression which contains coffiecients are variables.

• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.

• Quadratic polynomials are those polynomials which having highest power of degree as 2 .

• The general form of quadratic equation is ax² + bx + c.

• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.

6 0
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