5th Problem 2016

Algebra Level 2

Find the x - intercepts of the following function:

f ( x ) = 24 x 2 − 10 x − 21 f\left( x \right) = { 24x }^{ 2 } - 10x - 21

Check out the set: 2016 Problems

6 7 a n d 1 3 \frac { 6 }{ 7 } and\frac { 1 }{ 3 } − 5 6 a n d 4 5 \frac { -5 }{ 6 } and\frac { 4 }{ 5 } 7 6 a n d − 3 4 \frac { 7 }{ 6 } and\frac {-3 }{ 4 } 7 8 a n d − 9 11 \frac { 7 }{ 8 } and\frac { -9 }{11 }

Angela Fajardo by Angela Fajardo , 19, Philippines

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2 solutions

Prince Loomba
Dec 31, 2016

We know that the product of roots of a x 2 + b x + c ax^{2}+bx+c is c / a c/a , so multiply the denominators of the roots in options. Only 1 option leads us 24 24 . Thats the answer!

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The sum of both roots is 10 24 = 5 12 \frac{10}{24}=\frac{5}{12} and the only alternative which gives a denominator 12 12 is " 7 6 \frac{7}{6} and − 3 4 -\frac{3}{4} "

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1 more trick to eliminate other roots: product of their denominators, only one has 24!

Prince Loomba - 4 years, 5 months ago

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nice solution, Prince

Hjalmar Orellana Soto - 4 years, 5 months ago

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Thanks I shall post it I suppose

Prince Loomba - 4 years, 5 months ago

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