determine whether the values given against each of the quadratic equation are the roots of equation x²+3x-4 ; x=1, -2, -3
Answers
Answer:
Hii
Step-by-step explanation:
The discriminant is represented by Δ.
Δ = b² - 4ac = (-8)² - 4(1)(7) = 64 - 28 = 36
b. The discriminant tells you the type of roots. If Δ is negative, the equation has two complex root. If Δ is zero, the equation has one repeated root (also called a double root). If Δ is positive, the equation has two real and distinct roots. For real and distinct roots, if Δ is a perfect square (like 1, 4, 9, 16, etc) then the real roots are rational; otherwise they are irrational.
For this equation Δ = 36. So there are two real and rational roots.
c. The roots occur wher y = 0, so
y = 0 = x² - 8x + 7
(x - 1)(x - 7) = 0
x = 1, x = 7 are the roots
d. x = (-b ± √Δ)/2a = (8 ± √36)/2
x = (8 + 6)/2 = 14/2 = 7
x = (8 - 6)/2 = 2/2 = 1
f. The y-intercept occurs at x = 0
y = x² - 8x + 7 = (0)² - 8(0) + 7 = 7
g. y = x² - 8x + 7
y = (x² - 8x + ___ ) + ___+ 7
y = (x² - 8x + 16) - 16 + 7 = (x - 4)² - 9
h. Completing the square form is the same as vertex form. Change the sign for the number in parentheses to get the x-coordinate. The y-coordinate is the number outside the parentheses just as it is. The vertex is (4, -9).
I hope it helps you
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