draw the graphs of y=5x²-20x+15 and find zeroes in each case
Answers
Answer:
Two solutions were found :
x = 3
x = 1
Step-by-step explanation:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((0 - 5x2) + 20x) - 15 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-5x2 + 20x - 15 = -5 • (x2 - 4x + 3)
Trying to factor by splitting the middle term
3.2 Factoring x2 - 4x + 3
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3
Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -4 .
-3 + -1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -1
x2 - 3x - 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-3)
Which is the desired factorization
Equation at the end of step
3
:
-5 • (x - 1) • (x - 3) = 0
STEP
Two solutions were found :
x = 3
x = 1
EXPLANATION.
Graph of the equation,
⇒ y = 5x² - 20x + 15.
From this equation,
Factorizes into middle term split, we get,
⇒ y = 5x² - 15x - 5x + 15.
⇒ y = 5x (x - 3) - 5(x - 3).
⇒ y = ( 5x - 5)(x - 3).
⇒ ( 5x - 5)(x - 3) = 0.
⇒ x = 1,3.
Put the value of x = 1 in equation, we get.
⇒ y = 5(1)² - 20(1) + 15.
⇒ y = 5 - 20 + 15.
⇒ y = 20 - 20.
⇒ y = 0.
Their Co-ordinates = (1,0).
Put x = 3 in equation, we get.
⇒ y = 5(3)² - 20(3) + 15.
⇒ y = 45 - 60 + 15.
⇒ y = 60 - 60.
⇒ y = 0.
Their Co-ordinates = (3,0).
Put x = 0 in equation, we get.
⇒ y = 5(0)² - 20(0) + 15.
⇒ y = 0 - 0 + 15.
⇒ y = 15.
Their Co-ordinates = (0,15).
This equation forms parabola upwards graph.
