Find the values of and b for which x=2/3and x=-3 are the roots of the quadratic equations ax2+bx -6
Answers
Answer:
Step-by-step explanation:
put the values of the roots required
therefore 4a/9 + 2b/3 -6 = 0
also , 9a - 3b -6 = 0
4a/9 + 2b/3 = 6 ............................ 1
9a - 3b = 6 ...................................2
on solving a = 3
b = 7
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Answer:
Method to solve a quadratic equation by using quadratic formula.
Step 1. Write a given quadratic equation in standard form.ax²+bx+c=0 ,
Step 2.Find the value of a, b and c by comparing the given equation with ax²+bx+c=0 ,
Step 3. Put the values of a, b and c in quadratic formula i.e X=( -b +_ √ b²-4ac) /2a
By simplifying the above formula we get two roots…
This method is also called Sridharacharya’s rule.
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By using quadratic formula
(i) x-1/x = 3
⇒ x² – 3x -1 = 0
On comparing this equation with ax² + bx + c = 0, we get
a = 1, b = -3 and c = -1
By using quadratic formula, we get
x = –b±√b2 – 4ac/2a
⇒ x = (3±√9+4 )/2
⇒ x = (3±√13 )/2
∴ x = (3+√13 )/2 or x = (3-√13 )/2
(ii) 1/x+4 – 1/x-7 = 11/30
⇒ x-7-x-4/(x+4)(x-7) = 11/30
⇒ -11/(x+4)(x-7) = 11/30
⇒ (x+4)(x-7) = -30
⇒ x² – 3x – 28 = 30
⇒ x² – 3x + 2 = 0 ( by using factorisation method)
⇒ x² – 2x – x + 2 = 0
⇒ x(x – 2) – 1(x – 2) = 0
⇒ (x – 2)(x – 1) = 0
⇒ x = 1 or 2
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Hope this will help you
Step-by-step explanation:
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