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Answers
Answer:
b
Step-by-step explanation:
discriminant must be greater than zero
ax^2+bx+c =0
discriminant = b^2 - 4ac
(3k)^2 -4(4)(9) is greater than zero
solve
Answer:
(b). k > 4
Note:
★ The possible values of the variable which satisfy the equation are called its roots .
★ A quadratic equation can have atmost two roots .
★ The general form of a quadratic equation is given by ; ax² + bx + c = 0
★ The discriminant of the quadratic equation ax² + bx + c is given by ; D = b² - 4ac
★ If D > 0 , then the roots of quadratic equation are real and distinct .
★ If D = 0 , then the roots of quadratic equation are real and equal .
★ If D < 0 , then the roots of the quadratic equation are imaginary ( non-real ) .
Solution:
Here,
The given quadratic equation is ;
9x² + 3kx + 4 = 0
Clearly,
a = 9
b = 3k
c = 4
Thus,
The discriminant of the given quadratic equation will be given as ;
=> D = b² - 4ac
=> D = (3k)² - 4×9×4
=> D = 9k² - 9×16
=> D = 9(k² - 16)
Now,
For real and distinct roots , the discriminant of the given quadratic equation must be greater than zero .
Thus,
=> D > 9
=> 9(k² - 16) > 0
=> k² - 16 > 0
=> k² - 4² > 0
=> (k + 4)(k - 4) > 0
=> k > 4 or k < - 4
Sign scheme for k ;
+ – +
– ∞ <-----------( – 4 )------------( 4 ) ----------> ∞
But , observing the given options ,
The required answer is : k > 4
Hence,
k > 4