Quadratics? Again?

Algebra Level 2

5 x 2 − 34 x + 24 = 0 \large 5x^2 - 34x + 24 = 0

Find the larger solution x x to the equation above.


The answer is 6.

Factored Radical by Factored Radical , 21, USA

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2 solutions

Rahil Sehgal
Apr 5, 2017

Method1: 5 x 2 − 34 x + 24 = 5 x 2 − 30 x − 4 x + 24 = 0 5x^2-34x+24 = 5x^2-30x-4x+24 = 0

⇒ ( 5 x − 4 ) ( x − 6 ) = 0 \Rightarrow (5x-4)(x-6) = 0

Therefore the answer is x = 6 \color{#3D99F6}{ x= 6} .

Method 2: x = − b ± b 2 − 4 a c 2 a x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}

⇒ x = 34 + 26 10 o r x = 34 − 26 10 \Rightarrow x= \dfrac{34+26}{10} or x= \dfrac{34-26}{10}

Thus, the larger value of x = 6 \color{#D61F06}{ x = 6} .

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Factored Radical
Apr 5, 2017

5 (x – 4/5) (x – 30/5) = 0 Should be the simplified equation you get. From this you can simplify it further to: 5x^2 – 4x – 30x + 24 = 0. After this, you can easily solve for x. The two answers you get should be 4/5, 6. Since 6 is greater, 6 is the answer.

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