if sum of zeros of the quadratic equation k x square - 2 x minus 3 K is equal to their product find the value of k
Answers
Answer :
k = -2/3
Step-by-step explanation :
➤ Quadratic Polynomials :
✯ It is a polynomial of degree 2
✯ General form :
ax² + bx + c = 0
✯ Determinant, D = b² - 4ac
✯ Based on the value of Determinant, we can define the nature of roots.
D > 0 ; real and unequal roots
D = 0 ; real and equal roots
D < 0 ; no real roots i.e., imaginary
✯ Relationship between zeroes and coefficients :
✩ Sum of zeroes = -b/a
✩ Product of zeroes = c/a
________________________________
Given quadratic polynomial,
kx² - 2x - 3k
It is of the form ax² + bx + c
a = k , b = -2 , c = -3k
we know,
Sum of zeroes = -b/a
Product of zeroes = c/a
given,
Sum of zeroes = Product of zeroes
-b/a = c/a
-b = c
-(-2) = -3k
2 = -3k
-3k = 2
k = -2/3
The value of k is -2/3
Answer:
-2/3 is the correct answer