# Find the values of p for which the equation x² – (p – 2)x + 2p +1 = 0 has equal roots

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## Find the values of p for which the equation x² – (p – 2)x + 2p +1 = 0 has equal roots

**A.** (1, 2)

**B.** (21, 0)

** C.** (0, 12)

**D.** (4, 5)

**QUICK ANSWER…**

**C**

**DETAILS…**

**For any quadratic equation to have two roots that are exactly equal, b****²**** must be equal to 4ac. Let me explain:**

**Let’s say a quadratic equation is given as ax² + bx + c = 0, then according to the almighty formula,**

**squaring both sides, b****²**** – 4ac = 0 or b****²**** = 4ac**

**applying this to solve the question, we have:**

**x****²**** – (p – 2)x + 2p + 1 = 0**

**from this,**

**a = 1**

**b = -(p – 2)**

**c = 2p + 1**

**performing b****²**** = 4ac, we have:**

**(-(p – 2))****²**** = 4 ****×**** 1 ****×**** (2p + 1)**

**(p – 2)****²**** = 4(2p + 1)**

**(p – 2)(p – 2) = 4(2p + 1)**

**p****²**** – 2p – 2p + 4 = 8p + 4**

**p****²**** – 4p + 4 = 8p + 4**

**p****²**** – 4p – 8p + 4 – 4 = 0**

**p****²**** – 12p = 0**

**p(p – 12) = 0**

**therefore, p = 0 or 12**

**Now for the right answer to the above question:**

**Option A is incorrect.****Option B is incorrect.****C is correct. 0 actually gives equal roots of 1 and 1, while 12 gives equal roots of 5 and 5.****D is not the correct answer.**

**KEY-POINTS…**

**You may please note these/this:**

**For any quadratic equation to have repeated or equal roots, b² must be = 4ac, where a, b, and c are co-efficients according to ax² + bx + c.****If you love our answers, you can login to say hi to us at the comment section…**

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**/ culled from 2020 JAMB-UTME mathematics past question 08 /**