2nd Problem 2016

Algebra Level 2

Find the product of all the roots of the following equation: 6 x 2 + 5 x − 10 = − 19. 6x^2 + 5x - 10 = -19.

The product is in the form of a simplified fraction a b . \frac{a}{b}. What is a + b ? a + b?

Check out the set: 2016 Problems


The answer is 5.

Angela Fajardo by Angela Fajardo , 19, Philippines

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2 solutions

Akshat Sharda
Jan 2, 2016

6 x 2 + 5 x + 9 = 0 6x^2+5x+9=0

By Vieta's, Product of roots,

= 9 6 = 3 2 ⇒ 3 + 2 = 5 =\frac{9}{6}=\frac{3}{2} \\ \Rightarrow 3+2=\boxed{5}

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But the question is 6x^2 +5x +9..

.

Abhinav Koul - 5 years, 5 months ago

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Indeed it should be +5x and not -5x but the answer would still be the same. The product of roots is c a \frac {c}{a} with c = 9 and a = 6. So, c a = 3 2 \frac {c}{a}= \frac {3}{2}

Angela Fajardo - 5 years, 5 months ago
Nikhil Raj
Jun 5, 2017

6 x 2 + 5 x − 10 = − 19 6 x 2 + 5 x + 9 = 0 Let the roots be α and β . So, product of roots = α ⋅ β = 9 6 = 3 2 ( By Vieta’s Formula ) . A n s w e r = 3 + 2 = 5 6x^2 + 5x - 10 = -19 \\ 6x^2 + 5x + 9 = 0 \\ {\text{Let the roots be }} \alpha {\text{ and }} \beta. \\ {\text{So, product of roots}} = \alpha \cdot \beta = \dfrac{9}{6} = \dfrac{3}{2} \quad ({\text{By Vieta's Formula}}). \\ Answer = 3 + 2 = \color{#3D99F6}{\boxed{5}}

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