Photo AI

The equation $x^2 + (k - 5)x + 1 = 0$ has equal roots - Scottish Highers Maths - Question 2 - 2019

Question icon

Question 2

The-equation-$x^2-+-(k---5)x-+-1-=-0$-has-equal-roots-Scottish Highers Maths-Question 2-2019.png

The equation $x^2 + (k - 5)x + 1 = 0$ has equal roots. Determine the possible values of $k.$

Worked Solution & Example Answer:The equation $x^2 + (k - 5)x + 1 = 0$ has equal roots - Scottish Highers Maths - Question 2 - 2019

Step 1

Use the Discriminant

96%

114 rated

Answer

To determine if the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 has equal roots, we use the discriminant condition:

D=b2−4ac=0D = b^2 - 4ac = 0 Here, a=1a = 1, b=(k−5)b = (k - 5), and c=1c = 1. The discriminant can therefore be expressed as:

(k−5)2−4(1)(1)=0(k - 5)^2 - 4(1)(1) = 0

Step 2

Apply Condition and Simplify

99%

104 rated

Answer

Expanding the discriminant equation:

(k−5)2−4=0(k - 5)^2 - 4 = 0

Now, simplifying:

(k−5)2=4(k - 5)^2 = 4 Taking the square root of both sides:

k−5=2k - 5 = 2 and k−5=−2k - 5 = -2

Step 3

Determine Values of k

96%

101 rated

Answer

Now, solving the equations:

  1. For k−5=2k - 5 = 2, k=2+5=7k = 2 + 5 = 7

  2. For k−5=−2k - 5 = -2, k=−2+5=3k = -2 + 5 = 3

Thus, the possible values of kk are k=3k = 3 and k=7k = 7.

Join the Scottish Highers students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;