Find the roots of ht 27kt2 123t 28 The smaller root is Th

Find the roots of h(t) = (27kt)^2 - 123t + 28 The smaller root is The larger root is What positive value of k will result in exactly one real root?

Solution

h(t)=(27kt)²-123t +28

h(t)=729k²t²-123t +28

ax² +bx +c =0 ==>x=[-b+(b²-4ac)]/(2a),x=[-b-(b²-4ac)]/(2a)

t =[123+((-123)²-4*729k²*28)]/(2*729k²),t =[123-((-123)²-4*729k²*28)]/(2*729k²)

t =[123+(15129-81648k²)]/(1458k²),t =[123-(15129-81648k²)]/(1458k²)

smaller root is [123-(15129-81648k²)]/(1458k²)

larger root is [123+(15129-81648k²)]/(1458k²)

one ral root when (15129-81648k²)=0

k²=15129/81648

k =41/(367)

k=0.43