Math, asked by palpratap9831, 10 months ago

Find the values of and b for which x=3/4and x=-2 are the roots of the equation ax²+bx-6=0 Also explain how you have done don't see the answer of this question from your book and copy it here.

Answers

Answered by atahrv
1

Answer:

a=4 and b=5

Step-by-step explanation:

p(x)=ax²+bx-6=0

p(3/4)=a(3/4)²+b(3/4)-6=0

(9a/16)+(3b/4)-6=0

Taking LCM:-

9a+12b-96=0

9a+12b=96

3(3a+4b)=96

3a+4b=96/3

3a+4b=32---------(1)

p(-2)=a(-2)²+b(-2)-6=0

4a-2b-6=0

4a-2b=6

2(2a-b)=6

2a-b=3

Multiplying Both Sides by 4:-

8a-4b=12-----------(2)

Adding Equation(1) and Equation(2):-

8a+3a+4b-4b=12+32

11a=44

a=44/11

a=4

2a-b=3

2(4)-b=3

b=8-3

b=5

Answered by Anonymous
6

Answer:

a =4 , b =5

Explanation :

p ( x) = ax^2 + bx - 6 =0

p (3/4) = a × (3/4)^2 + b × 3/4 - 6 = 0

= 9a/16 + 3b/4 - 6 =0

= 9a +12b - 96 =0 (taking LCM )

= 9a+12b =96

= 3 (3a+4b)=96

=3a +4b = 96 /3

= 3a + 4b = 32 _____ (i)

p ( -2) = ax^2 + bx - 6 =0

= a × (- 2) ^2 + b × ( -2) - 6 =0

= 4a^2 -2b - 6 =0

= 4a - 2b = 6

= 2( 2a - b) =6

= 2a - b = 6/2 =3

= 2a - b = 3

Multiplying both sides by 4

8a - 4b = 12 ___(ii)

Adding equation ( i) and (ii) ,

3a + 8a + 4b - 4b = 32 +12

= 11a = 44

a = 44 /11 = 4

Therefore , 2a -b =3 = 2× 4 - b = 3

8- b = 3

b = 5

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