Question

Roots of Quadratics 50 PTS!!!

Answer 1

Answer:

ax² + bx + c = 0 is solved using the formula

 

Step-by-step explanation:

Answer 2

The values of k for the different quadratic equation solutions are as follows

a  the equation 2x² - x + 3k = 0 has two distinct real roots

• k < 1/24

b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots

• k = 3/5

ci the equation -x² + 3x + (k + 1) = 0 has real roots

• k > -3.25

d the equation 3kx² - 3x + 2 = 0 has no real solutions

• k < ± 1.633

How to solve quadratic equations to get different answers

Quadratic equations of the form ax² + bx + c = 0 is solved using the formula

$-b+\frac{\sqrt{b^{2}-4ac } }{2a}$     OR     $-b-\frac{\sqrt{b^{2}-4ac } }{2a}$

The equation b² - 4ac is called the discriminant and it is used as follows

To solve the equation and get two real roots: 2x² - x + 3k = 0

• b² - 4ac > 0

substituting the values gives

(-1)² - 4 * 2 * 3k > 0

1 - 24k > 0

1 > 24k

divide through by coefficient of k

k < 1/24

To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0

• b² - 4ac = 0

substituting the values gives

(-2)² - 4 * 5 * (2k - 1) = 0

4 - 40k + 20 = 0

-40k = -24

divide through by coefficient of k

k = 3/5

To solve the equation and get real roots  -x² + 3x + (k + 1) = 0

• b² - 4ac > 0

substituting the values gives  

(3)² - 4 * -1 * (k+1) > 0

9 + 4k + 4> 0

4k > -13

divide through by coefficient of k

k > -3.25

To solve the equation and get  no real solutions  3kx² - 3x + 2 = 0

• b² - 4ac < 0

substituting the values gives  

(-3)² - 4 * 3k * 2 < 0

9 - 24k² > 0

9 > 24k²

divide through by coefficient of k²

k² < 24/9

k < ± 1.633

Learn more about roots of quadratic equations: brainly.com/question/26926523

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