Question

Factorise 3x^2-11x+26 how to solve this question?
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Answer 1

Answer:

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Step-by-step explanation:

solution(s) found

See steps

Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

STEP

1

:

Equation at the end of step 1

STEP

2

:

3x2 - 11x - 26

Simplify ——————————————

x - 5

Trying to factor by splitting the middle term

2.1 Factoring 3x2 - 11x - 26

The first term is, 3x2 its coefficient is 3 .

The middle term is, -11x its coefficient is -11 .

The last term, "the constant", is -26

Step-1 : Multiply the coefficient of the first term by the constant 3 • -26 = -78

Step-2 : Find two factors of -78 whose sum equals the coefficient of the middle term, which is -11 .

-78 + 1 = -77

-39 + 2 = -37

-26 + 3 = -23

-13 + 6 = -7

-6 + 13 = 7

-3 + 26 = 23

-2 + 39 = 37

-1 + 78 = 77

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Polynomial Long Division :

2.2 Polynomial Long Division

Dividing : 3x2-11x-26

("Dividend")

By : x-5 ("Divisor")

dividend 3x2 - 11x - 26

- divisor * 3x1 3x2 - 15x

remainder 4x - 26

- divisor * 4x0 4x - 20

remainder - 6

Quotient : 3x+4

Remainder : -6

Final result :

3x2 - 11x - 26

——————————————

x - 5

See results of polynomial long division:

1. In step #02.02

Answer 2

Answer:

complex roots

Step-by-step explanation:

using the Quadratic Formula where

a = 3, b = -11, and c = 26

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 11)± \sqrt{ {( - 11)}^{2} - 4(3)(26)} }{2 \times 3} \\ x = \frac{11± \sqrt{121 - 312} }{6} \\ x = \frac{11± \sqrt{191} }{6} \\ \\ the \: roots \: are \\ x = \frac{11 + \sqrt{191} }{6} \: \: \: and \: \: x = \frac{11 - \sqrt{191} }{6}$

it has complex roots

Hope you get your answer