Answer:
Step-by-step explanation:
Solving quadratic equation using formula:
5x² - 6x - 2 = 0
a = Coefficient of x² = 5
b = coefficient of x = -6
c = constant = -2
Discriminant = D = b² - 4ac
= (-6)² - 4 * 5 * (-2)
= 36 + 40
= 76 > 0
So, the quadratic equation has two distinct real roots.
[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]
[tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]
x = 1.47 or x = -0.27
Answer: x = 1.5 or (-0.3)
b) x² + 3x = 40
x² + 3x - 40= 0
We can solve the quadratic equation using factor method.
Sum = 3
Product = -40
Factors = 8 , (-5)
When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).
Rewrite the middle term of the quadratic equation using the factors.
x² + 8x - 5x - 40 = 0
x(x + 8) - 5(x + 8)= 0
(x + 8) (x - 5) = 0
x + 8 = 0 or x - 5 = 0
x = -8 or x = 5
Answer : x = -8 , 5
