Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation 3x^2-48=0
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Equation 3x^2-12x=0
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Equation -4x=32
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Equation -5+2x=-2x-7
- Express {x} in terms of y where:
- -1*x-15*y=13
- -3*x-1*y=-9
- -4*x-12*y=13
- -19*x-15*y=15
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Identical expressions
- 4x^ two -15x+ nine = zero
- 4x squared minus 15x plus 9 equally 0
- 4x to the power of two minus 15x plus nine equally zero
- 4x2-15x+9=0
- 4x²-15x+9=0
- 4x to the power of 2-15x+9=0
- 4x^2-15x+9=O
-
Similar expressions
- 4x^2-15x-9=0
- 4x^2+15x+9=0
4x^2-15x+9=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = -15$$
$$c = 9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = \frac{3}{4}$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = -15$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-15)^2 - 4 * (4) * (9) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = \frac{3}{4}$$
Vieta's Theorem
rewrite the equation
$$\left(4 x^{2} - 15 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{15 x}{4} + \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{15}{4}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{15}{4}$$
$$x_{1} x_{2} = \frac{9}{4}$$
$$\left(4 x^{2} - 15 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{15 x}{4} + \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{15}{4}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{15}{4}$$
$$x_{1} x_{2} = \frac{9}{4}$$
Sum and product of roots
[src]
sum
3 + 3/4
$$\frac{3}{4} + 3$$
=
15/4
$$\frac{15}{4}$$
product
3*3 --- 4
$$\frac{3 \cdot 3}{4}$$
=
9/4
$$\frac{9}{4}$$
9/4
The graph