The number of equations of the form ax2 + bx + 2 = 0 that can be formed if the equation have real roots (a > 2, b < 6 and a and b are positive integers) is/are
Answers
D = b2 – 4ac
It is determined from the coefficients of the equation ax2 + bx + c = 0.
The value of D reveals what type of roots the equation has.
If D is greater than 0, we get real roots
For ax2 + bx + 2 = 0
The discriminant = b2 – 4(a)(2)
= b2 – 8a
Equating this to 0
b2 – 8a = 0
8a = b2
a = b2/8
a and b are positive integers and b is less than 6
the values that b can take include: 1, 2, 3, 4, 5
when
b =1, a = 1/8
b =2, a = 4/8 = ½
b = 3, a = 9/8
b =4, a = 16/8 = 2
b = 5, a = 25/8
The only value of b that gives an integer value of a is 4
Meaning there is only one equation that can be formed that satisfy this condition
Answer:
Since the value given here for "a" is >= (greater than or equal to) 2 and the value for "b" is <= ( less than or equal to) is 6 and for some value for "b" it is "0". Let us take an equation to understand better-
therefore the equation will be like - ax^2+c=0 (here, the value of b is taken 0).
For the above equation (i.e ax^2+c=0 ) let us put a question from the given value ("a" is >= (greater than or equal to) 2 and the value for "b" is <= ( less than or equal to) is 6) -
=> 2x^2 - 200 = 0
=> x^2 = 200/2
=> x = +-10
Hence we can say that the roots for this question is 2.
Step-by-step explanation: