(40) maths question. plz help

Because: y=kx^2 + 3x + 1 touch the x-axis, so, y= 0

A= coefficient of x^2
B= coefficient of x
C= coefficient of (x^0=1)

0= B^2 - (4) (A) (C)
0=(+3)^2 - (4) (k) (1)
0=9- 4k
4k=9
k= 9/4 =2.25

Hence, the value of k is 2.25.

consider discriminant of the equation, if it touches the x-axis then this implies there is a double root and therefore the discriminant will be zero .

in equation ax^2+bx+c = 0, discriminant is b^2-4ac
=> 3^2-4(k)(1) = 0
=> 9-4k = 0
=> k = 9/4