How do you solve 10x^{2}-27x+18?

Connor Randall

Connor Randall

Answered question

2022-01-22

How do you solve 10x227x+18?

Answer & Explanation

Messiah Haynes

Messiah Haynes

Beginner2022-01-23Added 7 answers

Step 1
f(x)=10x227x+18
is of the form
ax2+bx+c,
with
a=10, b=27 and x=18
The discriminant Δ is given by the formula:
Δ=b24ac=272(4×10×18)=729720
=9=32
Being a positive perfect square, f(X)=0 has two distinct rational roots, given by the quadratic formula:
x=b±Δ2a=27±320
That is:
x=3020=32 and x=2420=65
Hence f(x)=(2x3)(5x6)
Graph {10x227x+18[0.25, 2.25, 0.28, 0.97]}
terorimaox

terorimaox

Beginner2022-01-24Added 16 answers

Step 1
10x227x+18=0
We can first factorise the above expression and thereby find the solution.
Factorising by splitting the middle term
10x215x12x+18=0
5x(2x3)6(2x3)=0
(5x6)(2x3)=0
Equating each of the two terms with zero we obtain solutions as follows:
x=65, x=32

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