Solved: "How do you solve 10x2−27x+18?"

Connor Randall

Answered question

2022-01-22

How do you solve

10 x^{2} - 27 x + 18 ?

Messiah Haynes

Beginner2022-01-23Added 7 answers

Step 1

f (x) = 10 x^{2} - 27 x + 18

is of the form

a x^{2} + b x + c

,
with

a = 10, b = - 27

and

x = 18

The discriminant

Δ

is given by the formula:

Δ = b^{2} - 4 a c = 27^{2} - (4 \times 10 \times 18) = 729 - 720

= 9 = 3^{2}

Being a positive perfect square,

f (X) = 0

has two distinct rational roots, given by the quadratic formula:

x = \frac{- b \pm \sqrt{Δ}}{2 a} = \frac{27 \pm 3}{20}

That is:

x = \frac{30}{20} = \frac{3}{2}

and

x = \frac{24}{20} = \frac{6}{5}

Hence

f (x) = (2 x - 3) (5 x - 6)

Graph

{10 x^{2} - 27 x + 18 [- 0.25, 2.25, - 0.28, 0.97]}

terorimaox

Beginner2022-01-24Added 16 answers

Step 1

10 x^{2} - 27 x + 18 = 0

We can first factorise the above expression and thereby find the solution.
Factorising by splitting the middle term

10 x^{2} - 15 x - 12 x + 18 = 0

5 x (2 x - 3) - 6 (2 x - 3) = 0

(5 x - 6) (2 x - 3) = 0

Equating each of the two terms with zero we obtain solutions as follows:

x = \frac{6}{5}, x = \frac{3}{2}

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