if 2 is the root of quadratic equation 3xsquare+px-p=0and quadratic equation 4xsquare-2px+k=0 has equal roots find k
Answers
Step-by-step explanation:
2 is the root of quadratic equation 3x² + px - 8 = 0………….(1)
& 4x² - 2px + k = 0 has equal roots ………….(2)
On putting the value of given root i.e x = 2 in eq 1 .
3x² + px - 8 = 0
3(2)² + p(2) − 8 = 0
3 × 4 + 2p - 8 = 0
12 + 2p − 8 = 0
4 + 2p = 0
2p = - 4
p = - 4/ 2 = -2
p = - 2
Hence the value of p is - 2.
On putting the value of p = - 2 in eq 2,
4x² - 2px + k = 0
4x² - 2(- 2)x + k = 0
4x² + 4x + k = 0
On comparing the given equation with ax² + bx + c = 0
Here, a = 4, b = 4 , and c = k
D(discriminant) = b² – 4ac
Given : Quadratic equation has equal roots i.e D = 0
b² – 4ac = 0
4² – 4(4)(k) = 0
16 – 16k = 0
16 = 16k
k = 16/16 = 1
k = 1
Hence, the value of k is 1 .
★★ NATURE OF THE ROOTS
If D = 0 roots are real and equal
If D > 0 roots are real and distinct
If D < 0 No real roots
Read more on Brainly.in - https://brainly.in/question/2427512#readmore
Step-by-step explanation:
if it is use full plz like it and followfg
