All categories

3 years ago

The difference between the roots of the quadratic equation x^2−12x+q=0 is 2. Find q.

Mathematics

1 answer:

shtirl [24]3 years ago

5 0

Answer:

The required value of q is 35.

Step-by-step explanation:

Let α and β are the zeros of quadratic equation, x^2−12x+q=0.

It is given that difference between the roots of the quadratic equation x^2−12x+q=0 is 2.

Equation : α - β = 2

Equation : α + β = 12

Equation : αβ = q

We have to create an algebraic expression.

(a+b)² = (a-b)² + 4ab

(12)² = (2)² + 4q

144 = 4 + 4q

144 - 4 =4q

140=4q

q = 140/4

q = 35

Therefore, the required value of q is 35.

<u>Some information about zeroes of quadratic equation. </u>

Sum of zeroes = -b/a
Product of Zeroes = c/a

You might be interested in

Which set of ordered pairs could be generated by an exponential function?

klemol [59]

Answer: Third option.

Step-by-step explanation:

By definition, Exponential functions have the following form:

$y = ab^x$

Where "b" is the base ( $b > 0$ and $b\neq 1$ ), "a" is a coefficient ( $a\neq 0$ ) and "x" is the exponent.

It is importat to remember that the "Zero exponent rule" states that any base with an exponent of 0 is equal to 1.

Then, for an input value 0 ( $x=0$ ) the output value (value of "y") of the set of ordered pairs that could be generated by an exponential function must be 1 ( $y=1$ ).

You can observe in the Third option shown in the image that when $x=0$ , $y=1$

Therefore, the set of ordered pairs that could be generated by an exponential function is the set shown in the Third option.

4 0

4 years ago

Read 2 more answers

If a circle has a radius of 2 ft. is the circumfrence and area the same? Explain

romanna [79]

Answer:no

Step-by-step explanation:

The circumference and radius are different

8 0

3 years ago

Read 2 more answers

Factor Completely x^4-2x^2y^2+y^4

12345 [234]

<h3>Answer :</h3>

$\bf (x+y)^2(x-y)^2$

==============

<h3>Solving Steps:</h3>

===============

$\rightarrow \sf x^4-2x^2y^2+y^4$

<u>breakdown</u>

$\rightarrow \sf x^4-x^2y^2-x^2y^2+y^4$

<u>factor common term</u>

$\rightarrow \sf x^2(x^2-y^2)-y^2(x^2-y^2)$

<u>collect in groups</u>

$\rightarrow \sf (x^2-y^2)(x^2-y^2)$

<u>apply difference between two square method:</u> x² - y² = (x+ y)(x-y)

$\rightarrow \sf (x+y)(x-y) (x+y)(x-y)$

<u>simplify</u>

$\rightarrow \sf (x+y)^2(x-y)^2$

7 0

2 years ago

Estimate The Measure of The angle

Alborosie

310 is the estimate measure of the angle

4 0

3 years ago

The amount Alex eamed last week can be modeled by the expression 25 + 5n 295, where is the number of items he sold. Which number

Lena [83]

Answer:

Step-by-step explanation:

4 0

3 years ago