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3 years ago

Solve the following quadratic. `x^{2}\ +\ 4x\ +\ 1\ =\ 6`

Mathematics

1 answer:

Flauer [41]3 years ago

7 0

Answer:

x = -5 and 1

Step-by-step explanation:

1. Subtract 6 from both sides to get x²+4x-5=0

2. Factor the quadratic equation. Find two numbers that have a sum of 4 and a product of (-5). The numbers 5 and (-1) add to 4 and multiply to get -5

3. The factored equation is (x+5)(x-1)=0

4. Set each factor to equal zero and solve for x.

x+5=0 ... x=-5

x-1=0 ... x=1

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Find the sumofthe geometrical progression of five terms, of which the first term is 7 and the multiplier is 7.Verify that the su

777dan777 [17]

Answer:

The sum of first five term of GP is 19607.

Step-by-step explanation:

We are given the following in the question:

A geometric progression with 7 as the first term and 7 as the common ration.

$a, ar, ar^2,...\\a = 7\\r = 7$

$7, 7^2, 7^3, 7^4...$

Sum of n terms in a geometric progression:

$S_n = \displaystyle\frac{a(r^n - 1)}{(r-1)}$

For sum of five terms, we put n= 5, a = 7, r = 7

$S_5 = \displaystyle\frac{7(7^5 - 1)}{(7-1)}\\\\S_5 = 19607$

The sum of first five term of GP is 19607.

Verification:

$2801\times 7 = 19607$

Thus, the sum is equal to product of 2801 and 7.

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2 years ago

Solve the equation 4s2+32s=60 by completing the square

lord [1]

Answer:

s = -4 ± √31

Step-by-step explanation:

Given 4 $s^{2}$ + 32s = 60

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s = -4 ± √31

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