Use the discriminant to predict the nature of the roots, then use the quadratic formula to find the roots. 4x^2 - x - 5 = 0

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the formula of discriminant `Delta` , such that:

`Delta = b^2 - 4ac`

Identifying the coefficients a,b,c yields:

`a = 4, b = -1, c = -5`

Replacing the values of a,b,c in equation above yields:

`Delta = (-1)^2 - 4*4*(-5)`

`Delta = 1 + 80 = 81`

Since `Delta > 0,` hence, the quadratic equation has two different solutions. You may evaluate the solutions using the following quadratic formula, such that:

`x_(1,2) = (-b+-sqrt(Delta))/(2a)`

`x_(1,2) = (-(-1)+-sqrt(81))/8`

`x_(1,2) = (1 +- 9)/8 => x_1 = 5/4; x_2 = -1`

Hence, evaluating the solutions to the given equation, yields `x = -1, x = 5/4.`

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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`4x^2 - x - 5 = 0 ` use the formula `b^2-4ac` and plug in the numbers

`a=4`  ` b=-1 `   `c=-5`

`-1^2-4(4)(-5)`

`1+80=81 `   the discriminant is 81, since it is bigger than 0 it means it has 2 real solution, use the quadratic formula to find the roots

`(1+-sqrt(81))/(2(4))`

`(1+-9)/8`

`(1+9)/8 = (10)/8 = 5/4`

`(1-9)/8 = -8/8= -1`

the roots are -1 and `5/4`

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