Question

$4y \: square \: - y - 14 = 0$
​

Answer 1

Answer:

y=2. y=-7/4

Step-by-step explanation:

4y^2-y-14=0

=> 4y^2 - 8y +7y -14=0

=> 4y(y-2) +7(y-2)=0

=>(4y+7)(y-2)=0

y=2. y=-7/4

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Answer 2

Given:

$\\ \\ 4 {y}^{2} - y - 14 = 0$

To Calculate:

Value of y.

Answer:

$\\ \\ 4 {y}^{2} - y - 14 = 0$

Using Sridharacharya Formula,

$\\ \tt \: x = \dfrac{ - b \: \pm \: \sqrt{{b}^{2} - 4ac }}{2a} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\sf where \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\tt x \: = \: roots \: of \: the \: equation \: \: \\\tt a = constant \: in \: a {x}^{2} + bx + c \\ \tt b = constant \: in \: a {x}^{2} + bx + c \\\tt c = constant \: in \: a {x}^{2} + bx + c$

Here,

a = 4

b = -1

c = -14

Substituting the values of a , b and c , we get:

$\\ \\\sf y = \dfrac{ - ( - 1) \: \pm \: \sqrt{ ( - 1)^{2} - 4 \times 4 \times ( - 14) }}{2 \times 4} \\ \sf y = \dfrac{1 \: \pm \: \sqrt{1 + 224} }{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\sf y = \frac{1 + \sqrt{225} }{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf y = \dfrac{1 + 15}{8} \: \: or \: \: y = \dfrac{1 - 15}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf y = 2 \: \: \: or \: \: \: y = - \dfrac{7}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\sf y = 2 \: \: \: or \: \: \: y = - 1.75 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the answer is:

y = 2 or y = -1.75

Additional Information:

1) In Quadratic Formula, the value of a, b and c can be negative if the equation contains a , b and c with negative sign .

2) In some questions, if the value of root cannot be negative , then we neglect the negative value of root.

3) We take out the square root of discriminant in quadractic formula by Division Method. b²-4ac is called the discriminant.

4) If the value of discriminant is coming less than zero i.e. with negative sign, the roots of the equation become complex roots.