Question

the smallest integral value of k so that the equation 3x^2-4x+k=0 has no roots in R is..

a.0
b.
c.2
d.3

Answer 1

Answer.

GIVEN QUADRATIC EQUATION

$3 {x}^{2} - 4x + k = 0$



THE QUADRATIC EQUATION IS

$\frac{ (- b + - \sqrt{ {b}^{2} - 4ac }) }{2a}$

according to given statement the given eq have no root. so

USING DISCRIMINANT VALUE FOR NO ROOT



${b}^{2} - 4ac < 0$



GIVEN

a = 3. b =-4. c= k

put in discriminate value we get

${ (- 4)}^{2} - ( 4 \times 3 \times k) < 0$



$= 16 - 12k \: \: < 0$



$= - 12k < - 16$




$= 12k > 16$



$k > \frac{16}{12}$






$k > 1.33$


= > k =(1.33 , infinity )

Answer 2

Answer.

GIVEN QUADRATIC EQUATION

THE QUADRATIC EQUATION IS

according to given statement the given eq have no root. so

USING DISCRIMINANT VALUE FOR NO ROOT

GIVEN

a = 3. b =-4. c= k

put in discriminate value we get

= > k =(1.33 , infinity )